Often times, you see the flaw in someone else's thinking. You then conclude that they're wrong, and that the opposite is true.

People who believe in god are so stupid! They're wrong because X. God definitely doesn't exist.

But just because their logic was wrong, doesn't mean that their conclusion was also wrong. For example, I could believe that gravity works because the sky is blue. My bad logic doesn't cause gravity to stop working.

What you should do, is argue against yourself. People often derive their beliefs from arguments that they win against other people. You shouldn't do that. You should only derive beliefs from the arguments that you win against yourself.