People who put their view to another with a goal to change the other person's mind do tend to get worn out. Of course they do. It's the frustration of their goal that wears them out. If they believe the point of putting their view out there is to change minds, they're not going to change many, maybe not any, and so they'll judge all that effort wasted. Naturally, this will wear them out.
It's sad, because they clearly do care about right and wrong views of things. I'd like to think they do, at least.
There are at least 2 great reasons to put your view out to someone that blow away these puerile debate-clubbers' "mind change" fixations. One is because truth is a great and positive relief and release to share. Whether it's a joyful truth, or a truth of justice outraged, once you've really tapped that outlet it's way easier to let it out than shut it in.
The other is, you share yours to understand theirs. Not only the view of the human being across from you, but how they came to that view, and how they continue to hold it. Honest questions, with sincere interest in the answers: you'll hear so many different ways and paths. Even if the conclusion doesn't ever make sense to you, you will increasingly understand the people. That understanding can never be a detriment to your ability to engage with others, and speak truth to them. The more of them you understand, the greater your reach will be.
These goals don't rely on external reactions for their fulfillment. Instead of wearing out, you will grow in strength and purpose.
Another good reason. If all you care about is changing minds, winning the argument - the goals of the puerile debate-club crowd - people can sense that. They can tell your questions aren't serious, your views aren't open, and that to you, the whole thing is just some kind of competition.
Ironically, people who think it's all a waste of time unless you can change minds suck worst at changing minds. That's why you'll hear them so often, crying aloud at how useless it is to bother. They're right: and they speak for themselves.
Don't listen to them. Nobody should, really.