Daas Zekeinim m’Baalei Tosfos wondered how Avraham Avinu bypassed Yishmael and bequeathed all his possessions to Yitzchak Avinu. Yishmael was his son, perhaps one that did not engender much pride in Avraham, but his son nonetheless. Chazal (Kesubos 53A) teaches that one may not give to one child over another-even if the other son is of ill repute, because one does not know what offspring will descend from him. Avraham adhered to the entire Torah; he should have observed the laws of inheritance. They reply that Avraham and Yishmael were gerim, converts. Chazal (Kiddushin 1813) teach that a convert does not inherit his father.
In Nimakei Ridbaz, Horav Yaakov David Willowsky zl, explains that the Torah clearly writes, Ki b’Yitzchak yikarei lecha zera; “For Yitzchak will be considered your offspring”( Bereishis 21:12). This means that only Yitzchak’s progeny are considered Avraham’s descendants. Bnei Yishmael are not Bnei Avraham Avinu. Indeed, one who makes a neder, vows, not to have pleasure from zera Avraham is permitted to zera Yishmael. They are not our cousins! With regard to the Posuk in Vayera (Ibid 21:13), V’gam es ben ha’amah l’goy asimenu ki zaracha hu; “And also the son of maid servant I will make into a nation, because he is your offspring,” this applies only to Yishmael, whose mother, Hagar, had converted. It does not refer to Yishmael’s offspring who have no claim whatsoever to being descendants of Avraham. Once Yishmael married a gentile, the children that were born followed matrilineal descent- and are gentiles. The law concerning passing over one son for another exists, because we never know who will descend from him, applies only to one whose sons are Jewish-not to gentiles.