Acceptance vs approval

Something my therapist told me yesterday I'm still chewing on. Maybe you have some insight into it:

"Acceptance is not the same as approval."

He was explaining that my problem does not lie with self-acceptance but self-approval. I can completely comprehend the reality of my weight and other things and I do not challenge that they are what they are. However, I still strongly disapprove of myself for those things being as they are.

Likewise a person who is highly antagonistic towards gay people may in some cases completely accept the reality that their child is gay- but their disapproval could still lead them to shunning that child.