b/f versus c/c

[YourAce]

I have noticed in many post, that in certain cases, people have offered advice of a b/f on the river hu, when hero has a piece of the board and villain just called a bet or a raise on the prior street (turn), versus a play of c/c on the river. If you are willing to put out a bet, why not c/c to a) see what villain has b) possibly win the pot. I ask because maybe this is a flaw in my game, as I would normally c/c, if I feel I might have second best, versus b/f.
Once again, my thinking is if I am willing to invest a bet on the river, why not c/c versus, b/f?

Little insight on my play: 10/20 player. I am pretty much a tight player who will mix it up some what, but play ABC poker for the most part. I mentioned this to give you an idea of my play, and like I said, maybe the question I ask, is a glaring flaw in my game.

I’d appreciate clarification on the b/f versus the c/c and advice if I am wrong in this scenario?

THANKS!