Albert Barnes Commentary 2 Samuel 14:24

"And the king said, Let him turn to his own house, but let him not see my face. So Absalom turned to his own house, and saw not the king`s face." — 2 Samuel 14:24 (ASV)

Let him not see my face - We are not told why David adopted this half-measure. Possibly Bathsheba’s influence may have been exerted to keep Absalom in disgrace for the sake of Solomon.