Different take on his weakness -- what if it's feeling like he's losing control/respect/needs to lead? (Obviously, losing control of his powers can't be included)
Points to consider:
--He often makes snap decisions, but he hates it when other people (meaning David) do.
--He doesn't like that David is so good at convincing/inspiring the others. This could be because he feels threatened.
--As a teacher, an uncontrollable class would be a plausible fear
--He hates things he can't control, like contests or games of chance
Rebuttal to the inevitable counter-argument:
But he's not always in control of the situation! There are plenty of times where he nearly dies, etc.
At the end of Firefight, we realize he's amazingly powerful, more than any we've seen so far, including maybe Steelheart. There are plenty of times where things go wrong, but he's almost always made the decision to limit his powers rather than let them run free. I don't think anything in the series left him completely without that option.