i agree partially with both sides, you need to be honest, but there's no way you should leave it as a hanging negative, you should definately spin it around in some way, show some positive which is either the cause or result of the negative.
I've never gotten the "why not accept you" but I have had the "weaknesses" question. I said stubborness, then qualified it to what I think is sort of a misconception of stubbornness because I challenge people to provide good logical evidence in an argument for me to be convinced of their side. Often people percieve this as stubbornness when I mean to be simply intellictually challinging. I do know that I could, through changes in demeanor and tone, work to make my intentions of not being stubborn more clear to others.
That's the jist of what I've said to this question. So I take it from weakness, to potential strength, to things I could work on to improve that potential strength. I think this is a fair twist of the question.