I often find this distinction frustrating, in that people will sometimes jump to attacking what they believe is my relevance claim before making any kind of judgement on the truth or falsehood of my argument. And then they're wrong about the relevance claim. (if there even is one. Sometimes I'm just nitpicking.)

I have a sneaking, unverified suspicion that a lot of these cases of mutual misunderstanding are..."unconsciously deliberate" is the phrase that comes to mind, although that doesn't seem quite right. They're ways for both parties to walk away convinced that they're right, without either being required to legitimately engage (and thereby risk turning out to be wrong). For bonus points, both parties can honestly accuse the other of intellectual defection if they bring it up again later!