Q. How come Abraham Avinu, who kept the complete Torah including eruv tavshilin, gave all his possessions to his son Yitzchak, thereby violating the mitzva of yerusha, as Shmuel says (Kesubos 33a); Don’t take part in a transference of yerusha even from a bad son to a good one?
A. A number of answers are given; Rabbosenu Baalei Hatosafos explain that they were all converts and as the Talmud (Kidushin 17b) teaches; a ger does not inherit his father the ger.
Machane Yehuda (282) quoted by Yabia Omer (C.M. 8: 10: 2) maintains that it does not apply when the son removed from the inheritance is an idolater, as Yishmael was. .
Beer Sheva adds that the reason the Talmud gives is that one does not know if in the future, in another generation, a good son may result from this evil son. In Yishmael’s and his other children case, Avraham Avinu foresaw with ruach hakodesh, that there were not to be good descendants.(See also Igros Moshe C.M. 2: 50, as this principle applies today).
Maharsho (Chidushei Agodos – Sanhedrin 91a) opines that since Sarah Imenu was his principal wife, so was her son.
Horav Shlomo Miller Shlit’a pointed out to what the Mizrahi (ad loc.) and others explain, namely that the posuk itself dictated; Ki Beitzchak yikareh lecha zera – Yitzchak will be your son.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a