Me, once I've stated my case, and find that a specific poster is going to keep on disagreeing, no matter what I say, I gladly get the hell out of the conversation. No sense in beating my head against a brick wall when it's obvious that all your opponent wants to do is argue. But, that's me.
What is wrong with that Andrei is that it tacitly assumes that your "case" is valid and not dangerous to you or others. If a poster keeps on disagreeing with you it may be that he is trying to save you, or the others, from the danger he sees if you translate the case into action.
I see profound dangers to individuals and to society in teaching evolution to schoolchildren. I am prepared to listen to arguments which show that the dangers I see are a figment of my imagination and thus not to be taken seriously. If such arguments are not forthcoming or persuasive I have the choice of keeping on disagreeing or letting it go and by doing so becoming complicit in the risk of the dangers bearing fruit. Accusing me of last-wordism is merely an excuse to avoid facing up to the dangers I am pointing to and to pretend that they don't exist. The prospect of the dangers is, by your position, being put on Ignore. You have translated "not wanting to know" into "banging your head against the wall" and, by doing so, have made not wanting to know sound superficially sensible.
I would disagree with a woman who expressed a determination to have an abortion right up to the moment the doors of the abortion clinic were shut in my face and she translated the determination into action. Action being the real last word.
If your case is trivial there isn't much to be said.
I once tried to persuade a wilful young lad to forget his determination to buy a powerful motorbike. Even when he bought one and rode it in a way one might expect him to do I persisted in arguing that he should sell it. I failed. He not only killed himself later but also his sister.
I think the "case" is the crucial matter.