פירוש על בראשית 21:11

על אדות בנו ON ACCOUNT OF HIS SON — because he heard that he had taken to degenerate ways (Exodus Rabbah 1:1). The real meaning, however, is because she (Sarah) had told him to send him away.

AND THE THING WAS VERY GRIEVOUS IN ABRAHAM’s SIGHT ON ACCOUNT OF HIS SON. That is, for he had taken to degenerate ways. The plain meaning, however, is that he was grieved because she had told him to send him away. Thus the language of Rashi.
The correct interpretation appears to me to be that Scripture is speaking in honor of Abraham, saying that the reason why the matter was very displeasing to him was not due to a craving for his concubine and his desire for her. Therefore, if she had told him to cast out only the maidservant, he would have done her will. But it was on account of his son that he was very much incensed and did not want to listen to her. But the Holy One, blessed be He, told him that he should not resent it at all, neither for the son nor for the maidservant, and that he should listen to Sarah’s bidding for it is through Isaac alone that his name will be carried on, while Ishmael will not be referred to as his offspring. Now because Abraham feared lest an accident happen to Ishmael upon his sending him away, He told him that He will make a nation of him and He will bless him since he is indeed his son.

על אודות בנו. On account of his son. Abraham was afraid that the expulsion would result in Ishmael pursuing unwholesome activities because he felt rejected. He had to be concerned about this since Ishmael was his son after all.