So Solomon banished Abiathar from the priesthood of the LORD and thus fulfilled the word that the LORD had spoken at Shiloh against the house of Eli.
Abiathar and Joab were both aiding and abetting in Adonijah's rebellious attempt, and it is probable were at the bottom of this new motion made of Adonijah for Abishag, and it should seem Solomon knew it, Kg1 2:22. This was, in both, an intolerable affront both to God and to the government, and the worse because of their high station and the great influence their examples might have upon many.
Commenting on 1 Kings 2:26-34
Then tidings came to Joab,.... Of the death of Adonijah, and the deposition of Abiathar: for Joab had turned after Adonijah; publicly appeared at his feast, when he was saluted king by him, and others, and privately gave him advice in the affair of Abishag: though he turned not after Absalom; did not join with him in his rebellion, but faithfully adhered to David; and...
So Solomon thrust out Abiathar - This was for having taken part before with Adonijah, but by it a remarkable prophecy was fulfilled; see 1 Samuel 2:13-35 (note), and the notes there. God had told Eli that the priesthood should depart from his house; Abiathar was the last of the descendants of Ithamar, of which family was Eli the high priest.