It's easy to see that in this case, if your audience is also willfully ignorant, you will end up in a downward spiral where you just try to destroy your opponen

It's easy to see that in this case, if your audience is also willfully ignorant, you will end up in a downward spiral where you just try to destroy your opponent's credibility and reputation in a shouting match, regardless of what the factual reality is. You may have convinced the audience, but you ended up with a solution that doesn't work and is divorced from the real world. Is it worth it in the end?