When people say that, it still doesn't mean that "neither side is invalid". If you thought your argument was valid, and you are opposed to his argument, how can you think it's also valid?
If you had changed your mind somewhat so that you now admit his argument has validity, but that you still weight certain deciding factors differently than he does, you should say _that_, not the meaningless phrase I LART people for.
If you think that your argument is valid and his isn't, but don't want to be so blunt (because you're tired of arguing), then say that you just can't accept his point and you don't wish to pursue the matter any further at the moment (or ever, depending on your mood). Don't try to put a pretty face on the fact that you still think he's an idiot in that respect.
In any argument where both sides have flawless arguments, the weighting of factors is different. Such arguments are so incredibly rare that I doubt the question will ever arise with most people. But if it did, I think they would simply recognize the different weightings and be done with it (or argue the weightings).
In 98% of the arguments, however, at least one side has flaws. And usually cannot see them even when they are clearly spelled out. And it's never _your_ side, oh no. It's always the other guy. He's a right pratt. He probably thinks the government is putting Mad Cow extract in our drinking supply and he wears tin foil hats to block alien mind control rays. He's such a dork!
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