Why was it so grievous to Abraham to send Ishmael away?

The thing was very grievous in Abraham's sight because of his son Ishmael. Abraham loved Ishmael, yet he did not have the long-range concept of the Abrahamic covenant of a Messiah coming through his loins. Thus the demand to cast out the bondwoman and her son deeply pained him.

Les explains that Genesis 21 records the separation of Isaac and Ishmael. Sarah saw Hagar's son mocking and demanded Abraham cast out the bondwoman and her son, for the son of the bondwoman would not be heir with Isaac, the son of promise. Verse 11 says the thing was very grievous in Abraham's sight because of his son Ishmael. Les notes Abraham loved Ishmael, but he still did not have the long-range concept of the Abrahamic covenant of a Messiah coming through his loins. God then told Abraham not to let it be grievous because of the lad and bondwoman, and to hearken to Sarah's voice.

Genesis 21:11

And the thing was very grievous in Abraham’s sight because of his son.

Why was Abraham so grieved about casting out Ishmael?

Abraham grieved because Ishmael was his son, whom he loved, yet Sarah demanded that the bondwoman and her son be cast out so Ishmael would not be heir with Isaac, the son of promise. God then told Abraham not to be grieved but to hearken to Sarah's voice.