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. . . Isaac the son of Abraham; Abraham fathered Isaac (25:19)
The cynics of that generation were saying that Sarah had become pregnant from Avimelech, since she had failed to conceive in all the years she was with Abraham. What did G‑d do? He formed the countenance of Isaac to resemble that of Abraham, so that all might attest that Abraham had fathered Isaac. This is the meaning of the repetitious wording of the verse: "Isaac (is certainly) the son of Abraham, (since there is proof that) Abraham fathered Isaac."
(Rashi)
There are children who are embarrassed of their parents, and there are parents who are embarrassed by their children. With Abraham and Isaac it wasn't like that: Isaac prided himself in that he was "Isaac the son of Abraham," and Abraham prided himself in that "Abraham fathered Isaac."
(Midrash Tanchuma; Midrash HaGadol)