Why did the writer use "he' and not "him" in this sentence?
It is he whom the committee has chosen
That is a challenging question, indeed! Consider it this way.
Person One: "It is he!"
Person Two: "Who?"
Person One: "You know, the man chosen by the committee."
Person Two: "Oh, so he is the one whom the committee has chosen!"
Person One: "Yes, it is he whom the committee has chosen."
The point is that two independent clauses have, in effect, been joined together:
It is he.
The committee has chosen him (which, when you reverse it, becomes "whom.")
I hope that is helpful. Thank you for bringing this illuminating example.