“From my limited perspective, it’s actually quite rare for a child to be kicked out, but when it happens, […] it’s to protect other children from a negative influence.”
Just as in Yishmael’s case. Are you reading this, OP?
coffee addict:
I’ll take a shot at it. What was meant was not that this method of
dealing with Yishmael was chosen only for the purpose of working on Avraham Avinu’s balance of middos, despite what it might mean for Yishmael – rather, this was the proper way to deal with Yishmael, but Avraham was opposed to it because he was too far to the side of
chesed. Thus, he was correcting himself by doing what should
have been done regardless.