Not really, backing down is more often a cowards way out "I don't want any trouble" kind of decision. Occasionally it is a "...shit. I guess I was wrong..." decision. But more often than not it's the former. It's hardly a sign of maturity, if you back down when you know the other person's in the wrong that's not mature at all, it's you trying to go through your life avoiding conflict, something you need from time to time to learn about yourself and toughen up.
Then again maybe I say that because I can't stand backing down.
Then again maybe I say that because I can't stand backing down.