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!”).
In practice it isn't supposed to be like this. You should be working with your manager over 2 to 8 quarters or more to plan the promotion. The promotion will be won from a committee by your manager. The expectations should be clear.
Rejecting a promotion can be seen as bad in toxic places or for junior engineers, but I actually like hearing this from my reports because it means that I don't need to make changes to accommodate their growth.
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”.