can't becomeOften emphasizes that someone cannot become a particular kind of person or take on a particular role. In 気になれない, the expression means “can't bring oneself to” or “doesn't feel like.”
can't bring oneself toOften used in 気にはなれない to say someone cannot bring themselves to do something. With other nouns, it can mean “can't be” or “can't become” that thing.