Why was Avrohom afraid that the Egyptians would kill him for his wife Sarah?
(12,12) “When Avrohom was approaching Egypt, he said to his wife, Sarah: And it will be when the Egyptians see you…they will slay me and let you live.”
Since Avrohom’s main concern was that the Egyptians should not kill him, what are the meaning of his additional words “and let you live”? It seems to me that we can explain it, in the manner of an exposition, that with these words Avrohom was coming to answer the question which the commentaries asked - why was Avrohom afraid that he would be killed? Because either way you look at it, it should not have been a concern. Either the Egyptians kept the seven Noachide laws, in which case they would not transgress the command not to kill. Or they did not keep them, in which case they would readily transgress the command against forbidden relationships, and so it would not bother them that Sarah was married.
The various commentaries have already discussed this at length, each one in his way, but if seems to me that we can answer the question with the well-known words of the Parshas Derachim, that the reason why Avrohon threw himself into the fiery furnace, even though non-Jews are not commanded to give up their life rather than commit the sin of idol worship, is because he was concerned that he already had the status of a Jew when a stringency is involved, and thus he was commanded to give up his life in order to sanctify Hashem’s name.
Now, Avrohom understood that also Sarah would give up her life rather than commit a forbidden sexual act, and therefore he said to her "and it will be that when the Egyptians will see you" and will want to force you to have relations, and you will not wish to under any circumstances but instead you will give up your life, then the Egyptians will say that the reason is because you are married, and so they will have no recourse except to kill me, and through this “they will let you live”, since then you will not resist them.
Now everything makes very good sense, because in truth they did not keep the Noachide laws, and thus they had no specific need to kill Avrohom, since there was no difference to them between forbidden sexual relations and murder. But they would do so in order to keep Sarah alive, so that she would not give up her life since she was concerned that she had the status of a Jew. Therefore “please say that you are my sister”, and then even if you refuse to have relations with any of them they will think that it is because you don’t want to, and then “it will be well with me” - they will give me presents (as Rashi explains) to seduce you to choose one of them.
However, according to this we still have a problem, because the commentaries also asked why Avrohom did not simply divorce her - how could he allow himself to rely upon a miracle instead? They answered that divorce is not effective by non-Jews. But now, according to our words, the question returns - why did he did not divorce her? If we say that Avrohom and Sarah had the status of non-Jews, and that divorce is ineffective by non-Jews, then they are also not obligated to give up their lives, and on the contrary, according to the Rambam it is even forbidden to do so. If so, it follows that they would not kill Avrohom. And if, as was their concern, they had the status of Jews, then divorce would be effective and make her completely permitted, and so Avrohom should have divorced her and then he would not have needed to be afraid that they might kill him.
We can answer this fairly simply, that granted on the side of stringency they were concerned that they had the status of Jews, but where a leniency was involved they held that they had the status of non-Jews, and so divorce was ineffective. Therefore, even if the truth was that they had the status of Jews, nevertheless, since they were concerned that they had the status of non-Jews and in that case a get (a divorce document) would not release her to allow her to remarry, this factor is enough to invalidate the get since it can no longer be called a document which completely severs the marriage ties, and so it is not a get at all. Thus, if we say that divorce is ineffective by non-Jews, Avrohom had no option to use a get.
With this we can explain the posuk later on, when Phoraoh asked Avrohom “Why did you not tell me that she is your wife? Why did you say ’she is my sister', so that I took her to myself for a wife?”. It’s difficult to understand why Pharaoh also asked “why did you say she is my sister” - the main question was why Avrohom did not tell him that she was his wife! However, according to our words we can easily understand it. Pharaoh understood that Avrohom was afraid that they would kill him if they see that she was willing to give up her life. Therefore, Avrohom quickly said that she was his sister in order that they would not think that she was his wife, since non-Jews are not permitted to marry their sister.
But Pharaoh challenged him that since non-Jews are not required to give up their lives to avoid transgressing forbidden sexual relations, because non-Jews are not commanded to sanctify the name of Hashem, therefore perforce Avrohom must hold that they have the status of Jews. Now, it is clear that Terach did not have the status of a Jew, and so if we say that both Avrohom and Sarah have the status of Jews, it must be because they had come to recognise that they must serve Hashem, and so they are like newly converted converts. Now, we hold that the Torah permits a convert to marry his maternal sister (even though it is forbidden by the Rabbis), because a convert is considered as if has been newly born, and so is no longer considered a sibling. If so, even if Sarah was his sister she could be his wife.
Therefore, Pharaoh correctly challenged Avrohom that it did not help to say that she was his sister, because once the Egyptians will see that she is not willing to have relations with them even when there is a danger to her life, they would conclude that this is because she has the status of a Jew. And since her father clearly did not have the status of a Jew, she must be a new convert, and therefore even though she is his sister, she could be his wife, and so they would still kill him in order to get his wife. If so, Pharaoh asked, “why did you say 'she is my sister'”, since it was a pointless thing to say. This is a correct explanation in a manner of an exposition, to sharpen the minds of the students.