Okay, you are not thinking coherently. I never said being wrong made anyone a liar. I said that when X tells Y that what Y says isn't true, then X is saying that Y is lying. In the original post that Cozmo commented on, the OP was correct and Cozmo said that what the OP said was "not true". So, yes, again...Cozmo said he was lying and therefore called him a liar.
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Nope. If I say "Pearl Harbor happened in June of 1942" and you say "That's not true. It was December." You're not necessarily calling me a liar. You're saying I'm incorrect regardless of my intentions. You really shouldn't need this explained to you. And FYI, the OP WAS and still is incorrect.