Have you seen someone caught using poor logic to back up some kind of truth claim, who then jumps to a different, equally weak argument -- and they do it again, and again?
There's a great word for that: flailing.
People who are committed to their conclusion without investing much thought in it will try anything to justify it. You needn't to waste your energy trying to disprove all of their unserious arguments. Just point out they're flailing, and they're not convincing you.
People in this pattern are not truly convinced of their conclusion themselves.
This could/should be a moment of vulnerability, and possibly learning, but too often vulnerability is hidden under a shield of anger and aggression.
Telling someone who is activated like this that they don't believe their own conclusions is generally fruitless. That strategy is also too often weaponised within a heated argument.
But perhaps there's potential in asking what it would take to change their mind.
@BrentSullivan Yes, exactly. Sadly, while that's not actually true (ever!), if a person is so fully committed to the idea, or truth claim, or whatever, that they're protecting their self from even the awareness of that possibility, then there is no potential for any meaningful meeting of the mind.