there is likely nothing that is unsolvable given enough thought, trial and reflection.
Given our current political climate I have found what I consider to be the most solvable answer to those suffering from severe Trump Derangement Syndrome: this too will pass. They literally are tormenting themselves, there's nothing else you can really say to them that allows them a concrete solvable answer. What really kills me is when I am in a deep discussion with someone, (on another blog I blog on, things don't get to that depth here like a live active blog) and they respond back to me that they have presented their argument so there will be no need to respond back. If they didn't want to talk about it what are they doing on a blog. Of course I never pay any heed to them for all the reasons you have stated above.
So many are conflicted in their various positions that if you pay attention, you will see them realise while they are speaking that they are wrong. But, it doesn't stop them continuing.