A person’s idea does not end at the limits of their ability to articulate it. It does not end with the validity of the examples they use, nor does it end before the points that go unmade. An idea exists independent of that. Now, if we’re set that someone is wrong, because we know they are, then fine, this is what we do — use their flaws against them and never really think about it much. But if we’re having an interesting level of discourse and are trying to grow our understanding of a topic, we need to see deeper than what is presented to us.
A child wants to buy a $1.50 can of soda. His mother says he can’t afford it. He raises a dollar and 3 quarters and says “But I have two dollars!” The mother than says “No you can’t afford it because that’s wrong”. Just about anyone would get past the child’s statement and make their own deductions — that the child has $1.75 and thus has enough for the soda, but in a sense we are all, at some points, guilty of this — using an incorrect example or deduction as a reason to entirely falsify an argument.
Now, there is value to being logically right. It sends the other guy back to the drawing board to hopefully come back with better fleshed out ideas. But we, like our opponent, are capable of making those same logical deductions. This is why people complain about nitpicking — it’s a situations where technically something is wrong ( a weak example ) but people should be able to INFER the intent. Not so simple with complex system interactions, but we cannot be married to our positions so much that we neglect the ideas that are in front of us. The more often we can choke down our pride about being “right”, the more often we have a chance to learn something.