Albert Barnes Commentary 2 Samuel 16:21

"And Ahithophel said unto Absalom, Go in unto thy father`s concubines, that he hath left to keep the house; and all Israel will hear that thou art abhorred of thy father: then will the hands of all that are with thee be strong." — 2 Samuel 16:21 (ASV)

Taking possession of the harem was the most decisive act of sovereignty (see 1 Kings 2:22). It was also the greatest offense and insult that could be offered. Such an act on Absalom’s part made reconciliation impossible.

A further motive has been found in this advice: namely, Ahithophel’s desire to make David taste the bitterness of the cup he had caused others (like Uriah and all of Bathsheba’s family) to drink, and to receive the same measure of judgment he himself had dealt out.