I don’t understand what the Rabbi answered in answer #2.
The person asked why we study, and the Rabbi answered that there is value in the study itself. But that is exactly the question: what is that value?

First of all, I did explain. I wrote that study is cleaving to the Holy One, blessed be He (see Nefesh HaChayim, Gate 4, and Tanya, chs. 4–5).
I’ll explain further.
When you ask what the value of act X is, you assume there is some more fundamental reason, Y, that explains it. And if I then ask you what the value of Y is, and then keep asking like that, where does it stop? It stops at the most basic value, which itself requires no explanation. By the way, according to Leibowitz, that is the definition of a value: something that has no explanation outside itself.
My claim is that Torah study is the most basic value that explains other things. Therefore it itself cannot have an explanation outside itself. The Holy One, blessed be He, and the Torah are one, and therefore Torah study is cleaving to God.

Sorry, I still don’t understand. You said both that there is an explanation (“cleaving to God”) and that there is no explanation outside it.
So are there two explanations here?
And if the value of Torah study is cleaving, how is that achieved by study? It sounds like a pretty vague mystical explanation, certainly not something high schoolers will love. And the commandment of tefillin also leads to cleaving to God, so what is special about Torah study?

Studying Talmud is like preparing food: you invest time, work, and thought, and afterward the important part comes…

And some would explain that study is like preparation for birth: for 9 months the fetus develops, and afterward it comes out fully cooked…
Conclusion: whoever this doesn’t work for should buy prepared food or go to a surrogate mother.

Cleaving, my brother—that means wanting to understand the Creator and fulfill His commandments, and for that you need to learn His words.

I’ll give an example from morality. If you ask me what the value of human life is, what should I answer? Or alternatively, what is the value of preserving someone else’s property? What I can say is that human life is the highest moral level. That is not an explanation but a definition. I have not grounded the value of human life in some value called morality. Morality is not a value but the axis by which values are measured.
So too regarding Torah study. What I said is that this is cleaving to God at the highest level. Cleaving to God is the axis on which religious values are measured, and when I say that study is the highest cleaving to God, I am saying that this is the fundamental religious value, meaning that it cannot be grounded in something outside itself.

In other words, the Holy One, blessed be He, and His will (= the Torah) are one, and therefore Torah study is cleaving to God. This is not grounding one value (Torah study) in another (cleaving to God). It is identity, not grounding.

It sounds mystical to you because you assume that cleaving to God is an experience. But in Nefesh HaChayim it is explained that study is not a means to cleaving, but the cleaving itself. This is unlike Hasidism, where cleaving is understood as a religious experience, and study is a means to that experience of cleaving. As I said, in my view (following Nefesh HaChayim) this is not an explanation but an identity. So there is nothing mystical here. The logic is as follows: the Holy One, blessed be He = Torah (He and His will are one; it is the expression of Him and His will). Therefore engagement in Torah = cleaving to God.

Got it, thanks.
By the way, why are we sure that Torah study has more value than the other commandments—not quantitatively, because “Torah study is equal to them all,” but qualitatively? With tefillin we are satisfied that it is God’s will and a remembrance of the Exodus from Egypt, even if for someone it doesn’t evoke anything at all. So why, with Torah study, are we not satisfied to say that it is a commandment and that it will lead to knowledge of Jewish law, which really does seem to be the basis of the commandment—see Ezra? Maybe it’s only because people invest years in it? Shouldn’t this approach also be updated and slimmed down? What is it based on?

Torah study is not a means for knowing Jewish law or what to do. It is a value in itself. There are quite a few proofs for this. See Rashi at the beginning of Bechukotai, where he distinguishes between performing commandments, studying in order to do, and laboring in Torah for its own sake. Another proof is that women are obligated in the blessing over Torah study (as ruled by the Shulchan Arukh), and the Magen Avraham and Mishnah Berurah asked why they are obligated if they are exempt from the commandment of Torah study. They answered that women are obligated to learn the commandments relevant to them. From here we see that an obligation to learn the commandments relevant to you is still called being exempt from Torah study.
The strongest proof is the rebellious and wayward son, which according to at least one Tannaic opinion never existed and never will exist, and yet it is part of the commandment of Torah study. See the article by Rabbi Yisrael Salanter (in the collection of his essays published by Dorot Library) called “Statute and Judgment.”

So fine, let’s be satisfied with saying it’s one of the 613 commandments.

Absolutely not a commandment of the 613 in that sense. To fulfill the obligation of the commandment, it is enough for us to study one chapter in the morning and one in the evening (see Rosh and the commentator on Nedarim 7a, and elsewhere). Everything beyond that is, at most, a non-obligatory commandment according to the Rosh (and according to Ran, the result of a derashah). So the commandment aspect here has no special significance, and specifically the essential point is what matters. See the end of my article on reasoning:

סברות תורניות ומעמדן ההלכתי

See also the recorded lecture here:

Rabbi, it seems to me that this is a commandment among the 613 along the lines of “Know the God of your father and serve Him with a whole heart and a willing soul” and from “and to cleave to Him.”

http://wikivort.co.il/view.php?vort=1454

And even if in practice it isn’t counted, there is reward for study, as in: “Did not the Master say: Great is Torah study, for it leads to action.” So the reward for every commandment is included in the commandment itself, since he knew it and fulfilled it. And here we actually run into a small problem: you are still following the view regarding the rebellious and wayward son that he never was and never existed, but rather “expound it and receive reward.” But that would imply that you won’t receive reward, because it won’t lead to action, since there is no such case. Enough said.

The Master said this regarding all Torah study, not only commandments—derive from this that every matter of holiness that you learned, whether it is a commandment, or Jewish law, legal rule, deeds of the fathers, stories of the fathers, parables, words of wisdom, the history of our ancestors, proper conduct and manners…. all of it falls under Torah study.

If I may add some words from Prof. Yehuda Liebes, Israel Prize laureate in Kabbalah:

“It is worthwhile to study Talmud

To everyone I love who is interested in hearing my advice, I wholeheartedly recommend studying the Talmud. But not for the reasons already presented on the site. Not because it will help one find one’s bearings in our political and cultural world, nor for the sake of ‘building culture upon it,’ for I do not like the concept/institution of ‘culture’ at all, and I am not among its ‘consumers,’ and I am even somewhat anxious about what the Talmud can expect at the hands of that culture. Nor is the reason for the recommendation that the Talmud is a respected citizen in the ‘Jewish bookshelf.’ I do not belong even to the camp of devotees of that bookshelf, which seems to me like an ornate burial casket, into which they seek to place the Torah of life, the book of books of the people of the book, in the form of distinguished limbs bearing official approval. I understand the hearts of those who are alarmed by educators’ desire to load such a cabinet upon them, and for me too the Talmud is not at all a book on a shelf. In truth, for hundreds of years the Talmud lived and was created without being written down, dwelling entirely in the living minds of its creators and students, and this character is still evident on every page.
I recommend it because the Talmud is astonishing, and in my eyes there is nothing more beautiful or delightful than it; one can find in it consolation in old age, both the old age of the individual and of the people. It is a tremendous wealth kept by its owner for his harm—and I use this phrase not in the usual sense but according to its plain biblical meaning: wealth that continues to add to and support a person even when days of evil and old age come upon him, when it seems that he no longer knows what he is or what he will do in his world, as it is written: ‘Had Your Torah not been my delight, then I would have perished in my affliction.’ (I once heard from the Jerusalem poet Rivka Miriam, daughter of the Yiddish writer Leib Rochman, that she once found her father sobbing. She asked: Dad, what happened? And he answered her—and in Yiddish it sounded even sadder: It suddenly occurred to me: Oy, what does an ignorant person do in old age?!). We are the ‘owners’ of that wealth, and no one but us; this is the book into which our forefathers poured their lives. Many mighty nations may study the Bible, but very few will connect to the Talmud, which is a marvelous thing—I had written earlier ‘work’ and then regretted it, because of a certain embalming that rises from that concept—for which there is no brother or equal in the cultures of the world.
I cannot explain in advance the secret of the Talmud’s charm; for that one must taste it. And the truth is, I fear that even many veteran students will not understand what I am talking about, because they have grown accustomed not to seeing the Talmud as something beautiful, but as a difficulty that must be overcome (a difficulty that, in my opinion, has mainly been created by those who seek in it what is not there), or, worse still, as a spade with which to dig: solely for issuing halakhic rulings or for extracting intellectual ‘methods,’ and the like. Moreover, it sometimes happens that those who do not recognize the reality of the charm in the Talmud’s simplicity deliberately destroy it, by removing simplicity from its plain meaning, and thus that charm is lost to the learner in advance through their mediation.
As for the nature of this charm in my eyes, I will nevertheless try to give a hint: in the Talmud we hear the voices of wise and discerning people, but also direct and primal (primitive, in the foreign term), connected directly to themselves, their people, their Torah, and their God. They combine intellectual sophistication with a primitive directness than which none is greater (or lower). They speak in a simple popular language, in the dialect spoken in a remote province of the Persian and Byzantine empires (for us this indeed creates a certain difficulty), and they say in simplicity and directness the most intense and wondrous things, from an enormous sense of self-worth, yet one that is incidental and built in of itself. In their words and personalities, Jewish law and thought, aggadah, myth, and morality are all interwoven, to the point that the fields can hardly be separated. True, the world of those people is often far from what is accepted today, but precisely for that reason I find freedom and liberation in this study. Suddenly a person glimpses other possibilities and other worlds as well, beyond the wall of the totalitarianism of (post-)modern pluralism.
Perhaps something of the direction of my words may be understood with the help of the following famous example, from the Babylonian Talmud, tractate Megillah, 7b: ‘Rava said: A person is obligated to become intoxicated on Purim until he does not know the difference between “Cursed is Haman” and “Blessed is Mordechai.” Rabbah and Rabbi Zeira held the Purim meal together. They became intoxicated. Rabbah arose and slaughtered Rabbi Zeira. The next day he prayed for mercy on his behalf and revived him. The following year he said to him: Let the Master come and let us hold the Purim meal together. He said to him: A miracle does not happen at every hour and hour.’

Translation: ‘Rava said: A person is obligated to become intoxicated on Purim until he cannot distinguish between “Cursed is Haman” and “Blessed is Mordechai.” Rabbah and Rabbi Zeira held the Purim meal together, became intoxicated, Rabbah arose and slaughtered Rabbi Zeira. The next day he sought mercy for him and revived him. The following year he said to him: Please come, my friend, and let us hold the Purim meal together. He said to him: A miracle does not happen every time.’
End of his golden words.

Following what was said above regarding women’s obligation in Torah study, I came across a source in Sifrei from which it seems that there is an obligation of Torah study for women from the commandment “to serve Him with all your heart”:
In the Sifrei’s formulation: “‘And to serve Him with all your heart’—could this mean actual service?” That suggestion is rejected, and in its place come two other alternatives: “‘to serve Him’—this is study,” “‘to serve Him’—this is prayer.”

I didn’t understand the proof. How do you see from here that women are obligated? What we see here is that there is an obligation to study beyond the commandment of Torah study. That is true. You are assuming that women are certainly obligated in this commandment? Maybe yes, and maybe not. Even regarding Torah study itself I would assume that they are obligated.

What I meant is that there is a commandment to serve God with all your heart; that commandment applies equally to women and men (like other positive commandments that are not time-bound). The Sifrei says that this service of God is either prayer or Torah study. According to the second possibility, women are obligated in Torah study.

As I wrote, that does not seem necessary to me. After all, the regular commandment of Torah study is also not time-bound, and nevertheless women are exempt. The Sages apparently understood by reasoning that this does not belong with women (there are derashot, but it is clear that at their root there is a worldview). If so, the same could be said about the commandment “and to serve Him”: either women are not obligated in it, or women are not obligated in its study component, but rather each person serves God according to what is suitable and relevant to him or her.
As stated, perhaps one can indeed learn from here that there is another commandment to study as service of God beyond the commandment of Torah study. That was the basis for my claim.