Seeing as both Avraham (here) and Sarah (in 18: 12-13) laughed, why did Hashem take Sarah to task, but not Avraham?
Rashi, Targum Onkelus, 1 Ramban and Riva: Because whereas Avraham, who believed firmly in the prophecy that he would have a son, laughed out of pure joy, 2 Sarah laughed because she found the prophecy difficult to believe. 3
Ramban: Onkelus' source is that Hashem commanded to keep the name, in which case the laughter cannot have been imroper.
Targum Yonasan, in both places, translates the laughing as a laugh of surprise. It is not clear how he explains Hashem's different reactions to the two laughters.
Riva: Sarah laughed because she thought that it was a person's B'rachah. Avraham knew that it was from Hashem.
Bearing in mind that the earlier generations bore children as late as five hundred years old (e.g. Noach; see Bereishis 5:32), what was so surprising for Avraham and Sarah to bear children at a hundred and ninety, respectively?
Rashi: By the days of Avraham, the average lifespan had already shortened, and weakness had fallen upon the world. At their age, they were considered too old to have children.
Avraham already had a son (Yishmael) when he was eighty-six, so what did he mean when he exclaimed, "'ha'le'Ven Me'ah Shanah Yivaled?"
Ramban: Although it was possible for a man of a hundred to bear children, 1 it was amazing for him to begin to have children from Sarah, 2 after having lived with her for so many years without children.
Seforno: What he meant was that, under normal circumstances, a man of a hundred might well bear a child from a young woman, but not from an older one; and as for a woman of ninety, she could not bear children at all, even from a young man.
Lev Eliyahu (Shemos p. 131): The entire reason Avraham wanted a son was to continue teaching the world Hashem's ways. He was concerned lest he not live long enough to train him! He prayed that Yishmael, whom he had already trained for 13 years, would fear Hashem enough to be Avraham's spiritual heir. This is why Hashem responded, "v'Es Brisi Akim Es Yitzchak," i.e. Yitzchak will be Kadosh from the womb (Rashi to 17:19).
QUESTIONS ON RASHI
Rashi writes: "Although in prior generations, men would father children at 500 years, by the days of Avraham the average lifespan had already shortened..." Mizrachi asks
Gur Aryeh: Although Avraham himself was indeed fit to have children at that age, he saw that he was [by natural standards] unable to father children through Sarah. For any particular couple, the initial birth is what tips the natural balance and opens the way for more. It would be a great surprise if despite so many barren years of marriage to Sarah, and at his advanced age [when the body is naturally weakened], she would bear him their first child. To answer Mizrachi's first question, men generally do not father children while they are still growing, but rather after they are fully grown. The younger child-bearing age in the generation of Avraham shows that the generations were progressively weaker [and the proportion to the total lifetime is not relevant]. It would thus be a great surprise if at age 100, Avraham would have the ability to father children through Sarah for the first time.