The dimensions of the sermon

Shalu' Rabbi
We have now arrived at the study of the exemption from eating matzah during the days of Passover after the first Yom Tiv following the measure. Something that deviates from the rule is not studied for itself but rather to teach about the rule.
I'm trying to understand what the logic is in the measure. Why not say that when something is out of the ordinary, it alone is out of the ordinary. Why does it teach about the whole ordinary – so that all six days are gone?

After all, the Gemara has examples in both directions. Sometimes there is a verse from which we learn that the law is usually the opposite. And sometimes there are situations in which we learn from it a general parent construction. I usually explain that it depends on what we would say in the explanation: If we were to make a parent construction from the explanation, then we do. But if the explanation is the opposite of the verse, then we see it as an exception and learn that the general rule is the opposite.
Regarding something that was in general and then came out, this is a situation where a general is written and a detail is written that comes out of it. Here too, there are two interpretive options: either it comes to exclude or it comes to teach. Here, however, there are two options to explain why this option is chosen:
1. This is the agreed rule on which the Torah was written. God, the Holy One, gave us this standard in the Book of Mormon to say that we should interpret it this way and not the other way around. Therefore, such a standard is required in general and is not learned from logic.
2. Perhaps here too we can say that the matter depends on what the a priori explanation says (or interpretive explanation or the substance of the matter), and this is what determines the direction of the sermon (as I described above). A suggestion for such an explanation (this is interpretive explanation, of course): Since there is a GAZH of Tu-Tu (here in the Gemara a different teaching appears, and I did not check why. Surely the commentators comment) that says that the obligation is only on the first night, it means that on the other days it is permissible. Another possibility (also interpretive) is that "Ezeret" usually continues and completes what came before, and does not begin something new. Therefore, the interpretation that it comes to teach is preferred.
Of course, according to option 2, it follows that we will not always demand in a way that what is out of the ordinary is meant to be taught. This depends on the interpretation. However, according to option 1.
There is still more to discuss, since here the exception was not at all, since the verse speaks of the six days and not the seven. The Rabbinical Church truly writes that the rule is not the Risha of the verse but another verse, "Seven days you shall eat matzah," and now this is an exception to the rule.
Now I think that perhaps the "six days" in the verse cited here are the last six and not the first six (at least after the seventh one went out to teach, this shows that at the beginning of the verse it is about the last six, and not literally). And the seventh one was among them and went out to teach about them, everything is permitted. And this will explain everything, because there are two possibilities for reading the verse: either the six days are the first and then the last one went out to be an exception, or the six days are the last and the seventh one went out to teach. Since there is another verse that speaks of the seven days that unleavened bread is eaten, and there are makroth that exclude the first day (either Tu-Tu or those cited here), the way that the Sages chose is to read the six days as the last days.
I wrote all of this quickly without checking the commentators there. Of course, more research is still needed on all of this.
All the best,
Michi

Regarding the difference between what we have seen and the Deitztrich, the Maharsha Kiddushin 12:2 on Tosafot 3:1-3 suggests something different (perhaps contradictory). If the verse does not renew (for example, it says that a mission is not beneficial), then there is no benefit in building an ab and therefore one does the Deitztrich. If it renews, then one does the usual building an ab. I think this is a necessary and sufficient explanation.
If the explanation you propose to examine is one that is sufficient in itself to teach without a rabbi, then it is difficult to see why a father is needed, and a disagreement will also arise between you and the Maharsha. If it is a mediocre explanation, one that is not sufficient in itself to teach but is sufficient to support the teaching (such as Tosafot Shavuot 22:2, cf. Ibid.), then it seems that there is no disagreement between you and the Maharsha.

There is a lot to discuss about your words.
1. First, there is a difference between a situation where a verse is not renewed and a situation where a sermon is not renewed (see 2 below). A sermon that is not renewed is not difficult, since there is no difficulty in why the verse was written. And the sermon may also not be renewed (although there is a reference to the verse in which case there is a difficulty in the interpretation).
2. As in the rest of your statement. There is usually no difficulty in why a father's construction is needed, since the Torah did not write anything specifically for the father's construction. There is no deception in the father's construction, and the verse is written in its entirety. At most, one can ask why the Gemara needed to rely on a father's construction and did not settle for an explanation, but that is not that difficult. Even if it is possible to rely on an explanation, if there is a father's construction, the Gemara mentions this for reinforcement.
3. When there is a verse or sermon that teaches a law that is understood in explanation only after studying it (like what you called a mediocre explanation, although not exactly the same thing. It does not strengthen the study but rather explains it after we have studied it), then I would say that they are making a parent construction. And if the matter seems to be an innovation, then you have nothing to do with it except to innovate it and do what you read from Deitztrich.

So if I understand the matter correctly and am correct –
The Maharsha's test (the 'necessity test') is only relevant to referenced verses (and then if the verse repeats the ruling that came before it, then we learn 'from the Deitztrich' whether the explanation is with it or against it); and your test (the 'explanation test') is only relevant to non-referenced studies. And in fact, your words complement each other. Is that so?

I will cite the sources for ease.
Additions to the above-mentioned Kiddushin: And if you say, "My mother," it would not be better to send me to the holy places than to slaughter the bull of Aaron from Ditzreich, to say that it was in the possession of the owner, as it is written, and he slaughtered the bull of the sin offering that he had from among the holy places, not in their possession.
From the Maharsha: [The cutting of Aaron's fruit from the Deitztrich, etc., from the list of the other holy things, etc., etc.] Here is a question for Milph, what do we find in the rest of the holy things from the two owners of Aaron's fruit? Then I will not read it in full, because I gave it to them without the owners of the mission from them, etc.

indeed.
Indeed, my words are specifically about things that are taught in a seminar, and in such cases there is always a basis for them (otherwise there is no reason to study the verse specifically in this way). See, for example, the verse "Fear the Lord your God" in this article:
http://www.mikyab.com/#!%D7%A2%D7%9C-%D7%A1%D7%91%D7%A8%D7%95%D7%AA-%D7%9E%D7%A9%D7%9E%D7%A2%D7%95%D7%AA%D7%9F-%D7%95%D7%9E%D7%A2%D7%9E%D7%93%D7%9F-%D7%94%D7%94%D7%9C%D7%9B%D7%AA%D7%99/cu6k/5769345b0cf2644549bdacab
The example of Tos' and Mahrash seems like a study from the verse itself and not a midrash, since it is written in the verse that a mission is not beneficial (although there is room to push the verse in another way). Here there is a matter of deception if we were to study in the building of Av.