I'm going to guess you're an INTJ?

You highlight a very important point.

I try to set all of my ideas aside (except logic) and try to learn my debate partner's personal lexicon.

Once I feel like I have a basic understanding I will present a steel-man of their argument and ask, "is this what you mean?".

This is staking out common-ground. No real intellectual progress can be made until common-ground is agreed to.

MOST arguments (fights) are clear misunderstandings and miscommunications.

You might accuse me of being a COMMUNIST!!!

ANd when I ask you if you are accusing me of advocating STALINIST methodology (which I do not by the way), you refuse to make your personal definition of "communist" explicit and furthermore you take offense at me even asking the question, because, as you see it, "everybody knows what 'communist' means and you're just being dis-ingenuous if you pretend otherwise" (which is a classic rush-to-disqualify).

But more to your specific point, "...then it is almost a pointless discussion since that person has removed all constraints and can say anything they want."

This is actually not the case.

In the same way that you can analyze a fantasy-science-fiction book or movie for LOGICAL COHERENCE, you can temporarily adopt someone else's AXIOMS and try to point out where they CONTRADICT EACH OTHER.