Thank you very much for the answer,
Is it permitted to kill a Jew in order to save a non-Jew? Could I get a source, please?

Not merely permitted. Obligatory.
It seems simple to me as a matter of reasoning, and anyone who forbids it bears the burden of proof. After all, the entire law of a pursuer is fundamentally based on reasoning (and the sources they bring are of course not really sources).
Again, I saw a lengthy discussion by Rabbi Henkin, and in the end he arrives at this question. His conclusion is that if the government prohibited killing a non-Jew, then the law of a pursuer applies, and without that he remains uncertain. But what is doubtful to him is obvious to me.
See his words here: https://www.sefaria.org.il/Responsa_Benei_Banim%2C_Volume_III.44?lang=he

It should be added that the non-Jews of our time have the same status as a Jew for these matters, as the Meiri writes (among other things, one desecrates the Sabbath to save them). So sources that forbid it may perhaps be speaking about the non-Jews of ancient times.

I seem to remember from a few years ago that the Minchat Chinuch writes that there is no law of a pursuer here, but I need to look it up again. I don’t think the Meiri is relevant to this topic, because even he would agree that if one has to choose between a Jew and a non-Jew, the Jew’s life takes precedence. It seems to me that all the Meiri means to say is that whereas in the past non-Jews were considered wicked and prone to various transgressions, today that is not so, and therefore they are regarded as ordinary human beings. But they are still human beings, not equal in value to Jews. He too would of course agree that one is not executed for killing a non-Jew.

See the survey I sent. Almost all the sources are brought there.
How do you know that the Meiri would prefer the life of a Jew? True, from the passage in Horayot it appears that one should prefer that (because the non-Jew is obligated in fewer commandments), but that is not relevant to our discussion.
With “of courses” I don’t argue, of course (!).

Even if from a halakhic standpoint there is no law of a pursuer here, the massacre still has to be prevented by force of the law of the land.

There is also the question whether it is permitted to endanger soldiers in order to prevent harm to Arabs who are not involved in the fighting — something cowards have gone on about. And I thought that even if from a religious or moral standpoint it is forbidden, the state has the right to require soldiers to take risks for political reasons (war is the continuation of policy, Clausewitz and all that).

1. I don’t understand how, from the fact that by the law of the land it is forbidden to kill non-Jews, one can reach the conclusion that someone who does so is “rebelling against the government,” and from there go on to say that he may be killed.
2. The Meiri — I claim that his novelty is that the non-Jews in the days of the Sages were different from those of today, and therefore we do not regard them as wicked people and apostates. But nowhere did he innovate that they are equal in value to Jews, and if that is your claim, then the burden of proof is on you.
3. I just checked the source you referred me to, and indeed the Minchat Chinuch argues that there is no law of a pursuer when a Jew is pursuing a non-Jew.
4. Regarding the “of course” — I wrote: “He too would of course agree that one is not executed for killing a non-Jew.” As far as I know, there is no opinion that holds that a Jew who killed a non-Jew is liable to death, and that is what I meant when I wrote that the Meiri would agree. Isn’t that self-evident?
5. As for your reasoning — to me it is not simple at all (from a halakhic perspective, of course, not a moral one). How is it simple to you, as a matter of reasoning, that it is permitted to kill a Jew directly in order to save a non-Jew?

1. The claim is that he has the status of a pursuer by force of the law of the land.
2. He writes that it is permitted to desecrate the Sabbath for them. But as I said, in my view this is simple reasoning. If you think otherwise — fine by me, but you asked for my opinion, so I answered.
4. It has nothing to do with liability to the death penalty. We are talking about the law of a pursuer. Even a minor who murdered is not liable to the death penalty, but the law of a pursuer still applies to him.
5. It is not a matter of killing a Jew in order to save a non-Jew, but of killing him in order to prevent him from killing the non-Jew. The pursuer is responsible for the loss of the non-Jew’s life; he is not simply being put to death in order to save a non-Jew who has nothing to do with the situation.

4. The comparison to a minor is really not clear. Obviously the law of a pursuer applies even to someone who cannot incur the death penalty in a religious court. I was talking about the pursued person — what I wanted to argue is that since a Jew who killed a non-Jew would not be liable in a religious court, but if he killed a Jew he would be liable to death, that definitely lowers the status of the non-Jew’s life (even though it is still forbidden to kill him). If so, it is a major novelty to say that one may kill a Jew who is pursuing a non-Jew, and in my opinion a source is required for that. Why are you willing to accept that the Torah did not make the murderer of a non-Jew liable to death (in fact, to anything at all, right?), but when it comes to the law of a pursuer it is obvious to you by pure reasoning that his law should be exactly the same as if the pursued person were a Jew?

5. Sorry, I’m not sure I understood. If I understood correctly after all — are you claiming that the law of a pursuer is something like “separating a person from prohibition,” and not life-saving? That contradicts all the sources from which they derived the law of a pursuer (and even according to your approach, that the sources are more like supports, it is still difficult — they do not fit the case under discussion).

4. I thought you were talking about the pursuer.
My claim is that the law of a pursuer is not connected to the question of whose blood is redder, and therefore even if the Jew’s blood is redder than the non-Jew’s, the law of a pursuer still applies. Beyond that, Rabbi Soloveitchik on Maimonides explains that the law of a pursuer has two components: the pursuer has no blood-protection, and the saving of the pursued person. By virtue of being a pursuer, his blood is less red, regardless of the identity of the pursued person.
5. That is Rashi’s approach, but I did not write that. I was speaking about saving the pursued person, not saving him from sin (which, as stated, is Rashi’s approach, and even there, in my assessment, that is only an addition and not the whole law).

4. If the issue is not whose blood is redder, then why indeed do we kill the pursuer? Just because he is doing something forbidden? What is the reasoning at the base of this law?
6. Returning to my original question — according to the Minchat Chinuch, who holds that there is no law of a pursuer when a Jew pursues a non-Jew, what would be the answer to the two original questions I asked?

4. It is reasoning as plain as an egg — and not for nothing is it accepted throughout the entire world. We do not kill him because he is doing something forbidden. We do not kill someone who desecrates the Sabbath in order to save another person whose life is in danger. We kill him because he is the one who created the situation, and therefore the responsibility to fix it rests on him. That is exactly the difference between the law of a pursuer and the rule that one must be killed rather than commit murder. In both cases, it is Reuven’s life against Shimon’s life, and seemingly the rule is that one person’s blood is not redder than the other’s. And yet in the case of a pursuer, we kill one in order to save the other. Why? Because the equation that forces us to choose between them was created by him. So let him bear the consequences.
And that same reasoning, which is accepted throughout the entire world, exists regardless of the identity of the pursuer and the pursued — Jew, non-Jew, or Belgian. Therefore, by pure reasoning, the law of a pursuer applies in all cases, and the burden of proof rests on whoever wants to exclude a case from that reasoning.
These really are simple points, and I do not understand why we are getting tangled up here.
6. I didn’t understand question 1. If there is no law of a pursuer, then there is no law of a pursuer. As for question 2, I think not necessarily. The Arab would be permitted to do so, even if you are not, so there is no justification for killing him. The Jewish pursuer brought himself into a situation of coercion and danger, and no one else needs to pay for that with his life.
But as I said, the words of the Minchat Chinuch seem unfounded to me, and therefore I do not see much point in chewing them over.

4. I don’t understand the comparison to the world — throughout the world there is no difference between a Jew and a non-Jew, but in Judaism there is. Throughout the world, one who kills a Jew or one who kills a non-Jew would receive the same punishment in court, so there is no difficulty for them. You are consistently ignoring the fact that in the Torah world a non-Jew’s life is of lesser value than a Jew’s. Even you would agree that there is no law of a pursuer when a Jew is pursuing an animal. Even though he brought himself into that situation and really he is the one in the wrong here, still, since an animal’s life is less important than a human life (all the more so a Jew’s), we would not kill him. Why is that different from pursuing a non-Jew? Why is it not reasonable there to say that the Jew is indeed wicked — he is trying to kill a human being — but nevertheless we do not kill him?

You are consistently ignoring what I am writing.
I’m done.

I don’t understand. Did I write something disrespectful?

Did I write that you wrote something disrespectful? Again, you’re not reading.

Give me credit that I can at least follow one sentence. I assumed that from the way you paraphrased my words, from the ignoring of the question about the law of a pursuer regarding an animal, and from the “I’m done.” Not important — let’s really end it here.