"You're wrong" implies "you're a liar," or a more direct response could be "that's a lie." If the goal is to make someone look stupid, this can work better. Admittedly that's not always a major goal, cases won't overlap, etc.

But I think we do see people make fact-citing arguments that are delivered in the tone of "that's offensive", so the methods aren't mutually exclusive. For example, any argument beginning "There is no scientific evidence that..." in an appropriately shrill tone sends the message that offense is taken and sidesteps the logical evidence to highlight the strongest available evidence, the absence of scientific evidence.

Even if the offense argument is explicit, factual arguments could at least be added to it.