I suppose that is why I'm confused when the term is used, since I don't think I would use the term critical thinking for avoiding logical fallacies. A better term might be "not wrong thinking". Of course this also should take into account that some things we call logical fallacies probably shouldn't be considered logical fallacies at all, like "slippery slope" arguments and so forth, which are considered to be a fallacy since there is no mathematical implication, despite the obviously correct nature of many slippery slope arguments.
The word critical implies some sort of criticism, I'm not sure if identifying a logical fallacy is really what we typically mean by criticism. At the end of the day I guess the word itself isn't important.