There are a lot of simple ways to tell when your argument is wrong. There is one very specific on that I see all the time, and I want to talk about a bit more:
You try to tell other people what your opponent believes. *
* Exception - if you are an actual telepath and really can read minds, then tell me what your opponents think. Also, I have some questions about what my last date was thinking.
People do this all the time. It often happens when someone is proven wrong and is too arrogant to admit it. So instead of trying to figure out where they made a mistake, they look for a 'mistake' their opponent 'must have made'. Sometimes their opponent really was an idiot, and their own prejudice makes them think that all/most/many of their opponents must be that stupid.
Sometimes they were the idiot who totally failed to understand their opponent's intelligent argument. Instead they of understanding what their opponent really said, they twist it around to something idiotic. If I say "We evolved from primates", and some fool responds "Take that back about my mother!"
Note, if most of your opponents are that stupid, why didn't you win? When an adult can't beat an 'idiot', there must be something seriously wrong with the adult, or that 'idiot' is a lot more competent than you think.
So never talk about what your opponent believes - it always means you are wrong.
If you want to find out what your opponent believes, ASK THEM. If you want to write about it, look for something they said in print and you can point at and prove that particular opponent wrong. Why in print? Because that increases the chances you are talking about a belief held by more than just one strange guy.
More importantly, it doesn't matter what your opponent believes. Just because your opponent's argument is wrong doesn't mean you are right. Most of the old Fairy Tales were lies expressly to children in order to get them be good. There may not be a witch in the woods, but the kid still should NOT go into the woods. Bears may not have houses, but don't break into them, eat their food, and sleep in the beds.
So don't tell me what other people think, tell me what you think. Otherwise I will laugh at you for the arrogant, prejudiced, fake telepath that you are claiming to be.