What was Avraham trying to achieve by claiming that Sarah was indeed his sister?
Rashi: Avraham was pointing out to Avimelech that he did not lie outright, in that his claim was partially true.
Seforno: He was incriminating Avimelech, by blaming him for taking Sarah without inquiring as to whether she was not his wife too. 1
How could Avraham claim that Sarah was indeed his sister in order to substantiate his initial claim? Why would that not be incest?
Rashi and Rashbam: Assuming the Avos to have been considered Bnei-Noach, it was not incest, since a paternal relative of a Ben-Noach is not considered a relation (and Haran was Avraham's brother from another wife of Terach).
But Sarah wasn't Avraham's sister; she was his niece (his brother's daughter)?
Rashi and Rashbam: It was perfectly correct to claim that she was his sister, due to the principle 'grandchildren are like children' (in which case Haran's daughter was akin to Terach's daughter). 1
Gur Aryeh: Now that the danger had passed, surely there was no more cause to lie! Rashi therefore explains that Avraham's statement was true; Sarah was the daughter of Haran, and granddaughter of Terach, making her as if Avraham's sister.
What point was Avraham making? Seeing as he had caused Avimelech to sin, what difference did it make whether his claim that Sarah was his sister was true or not?
Ramban: Countering Avimelech's question why he tricked him, based on the fact that he (Avimelech) did not make a habit of taking people's wives, Avraham answered that, not knowing the ways of Avimelech, he was merely following a pact that he had made with Sarah, as he goes on to explain - not because he had seen anything that would implicate them, but because most countries through which he passed lacked Yir'as HaSh-m.
QUESTIONS ON RASHI
Rashi writes: "'She is my sister... he answered thus to verify his [original] words." Why did Avraham have to verify anything? He had just said that he would have been killed had he told the truth (20:11)!
Gur Aryeh: Avimelech could have countered that perhaps the populace was not entirely wicked, and by declaring her as his sister, he was putting a stumbling-block before the righteous men among them. Avraham therefore added in this verse that what he said was truth, for she was his "sister" in addition to being his wife. 1 Any man could have clarified further if he so wished.
Rashi writes: "'But not my mother's daughter' - Haran was from a different mother [than Avraham]." Why is this relevant, if Avraham's argument was that she was his half-sister?
Gur Aryeh #1: According to Rashi, Avimelech understood that Sarah was literally Avraham's sister, and not his niece. Avraham had to explain that they did not have the same mother and she was therefore permitted.
Gur Aryeh #2: Alternatively, Avraham was now explaining exactly that. "Daughter of my father" is a general term for a close relative (as family pedigree follows the father); "... but not the daughter of my mother," i.e. not literally my sister.
