But God said to Abraham, "Do not let it be displeasing in your sight because of the lad or because of your bondwoman. Whatever Sarah has said to you, listen to her voice; for in Isaac your seed shall be called. Yet I will also make a nation of the son of the bondwoman, because he is your seed." So Abraham rose early in the morning, and took bread and a skin of water; and putting it on her shoulder, he gave it and the boy to Hagar, and sent her away. Then she departed and wandered in the Wilderness of Beersheba. (Gen 21,12-14)
When we read about such treatment of people, we think it corresponds more to an effort to get them out of the way forever than dealing with one's own son. After all, Abraham was, as we know from earlier, "very rich." He could easily have furnished Hagar and Ishmael with provisions on several camels, and placed his servants at his command for escort and protection, and yet he does not seem to have done anything that would have saved them with certainty from perishing.
Such a proceeding was contrary to the custom of the time. He might therefore have counted on the fact that if Hagar and Ishmael eventually found refuge with the surrounding tribes, it would not make him popular with them (to put it mildly). What kind of man drives his own son into the desert? Abraham enjoyed respectability with the neighboring tribes, not only because of the supernatural intervention of his God with Abimelech, but generally by the way he conducted himself among them, keeping his farm, keeping the agreements he made, etc. If, after much deliberation, he decided to take such a drastic step, there must have been something fundamental behind it.
Ishmael must have been perhaps 15-16 years old at this point. For we know that he was 13 years older than Isaac, who had just been weaned, which was common only after a few years. (This is also why I choose the text correction "he put it on her shoulders" instead of "he put the child on her shoulders" in the quoted text.) Ishmael was by this time already physically mature and apparently capable of anything.
Abraham eventually gave in to Sarah's insistence, but apparently it wasn't just because she drove him to do so. We know that he was very distressed about it; he was about to do something he didn't quite want to. Sarah's request was so strange to him that he eventually sought God on the matter.
From all this we may conclude that the reason for the situation, namely, Ishmael's action towards Isaac, was indeed extremely serious, and his jealousy towards the child obviously dangerous. Peaceful coexistence was unfortunately out of possibility here. Ishmael had to go away.
