This is an extremely debated topic/question. Akin to "what came first, the chicken or the egg?" Anyway, my son is also a C (only in HS). He has always been a good hitter ever since he was little. And he has always wanted to catch, ever since his first year in T-Ball. While hitting is key to him (he currently hits in the 3 or 4 spot and leads the team in hits and rbis), I think more important to him are his pitchers and taking care of them and making sure he calls the best game he can (yes, his HS coach allows him to call many of his own games), and blocks everything that goes awry, throws out all the runners he can, etc. He has had (and played with) major bruises all over his body, jammed fingers, etc. - everything that goes with the job. He has a wide body, and so... He knows that good pitching will beat good hitting, always, and feels that he is key in this contribution. He is smart and works the psychological portion of the game well - I cannot recall ever seeing him really rattled, he is very calm as a general rule behind the dish (of course if he gets a big hit, like driving in the game winning run, then he goes nuts!) He also knows that catchers take a lot of the heat when things go wrong and get very little of the glory, and he's ok with that.
I sort of think that he thinks of hitting as the "more relaxed" portion (if that is the right way to put it) of his job, but he knows that without good defense, his team might lose more games than win - others on the team can hit, only he does the catching and is the ultimate last stop for runs coming across the plate.
I also believe that catching tools generally go in this order (and I think my son's tools fall into line this way, because he has always been a catcher and knows to work on his tools in this order)
1. arm strength (we are lucky, this is also my son's top tool)
2. fielding (again, lucky, probably his second best tool)
3. hit for power or average (he currently hits more for average, but can also hit for power)
4. foot speed (my son is ok fast, not the fastest, not the slowest)
Does this make any sense?