I think it would be a mistake to presume that he does not want the job. Instead, over the last several days multiple media reports suggested a “short list” of candidates Kamala Harris was considering; and none of these most recent lists included Cooper. Harris apparently saw more political benefit in choosing someone else.
Cooper therefore withdrew to avoid the appearance that he was not chosen.
It is speculated that he plans to run for US Senate against Thom Tillis in a couple of years. He would be awful for that position also. But his withdrawal keeps his appearance “unsullied” in the event he pursues that race later. He would not be the guy who was “passed over” by dear Kamala.