The problem with offering promotions to people already in your company is: what if they don’t actually want the promotion? (Promotions involve more responsibilities and not everyone wants that). And usually, Rejecting a promotion is seen as a bad thing (“oh, Joe doesn’t look ambitious enough!”).
The thing is: not everyone wants to be a “leader”, and rejecting a promotion is basically saying “goodbye” to be company that is offering you the promotion. I was in this exact same situation: I ended up quitting because I’m not a “leader”.