Why does Eggers take the blame for Anson's murder when he didn't do it?

One aspect of Eggers’ behavior that is left in question is why he admitted to having killed Anson when Delia was actually the one who committed the murder. Hester contemplates that perhaps Eggers really loved Delia and wanted to protect her from the fallout of Anson’s murder even though it was self-defense. Another way to rationalize Eggers’ motives might be that he saw what had happened as a way to keep both Dash and Delia in his control.