If it does win over the rational argument it's because it's being repeated and pounded more into their heads than the rational one.
You can't fight reality. Even the dumbest of the dumb will try to turn if they keep hitting a wall. But with all things being equal, the rational argument will have the advantage.
Take religion as an example. Its message is extremely appealing which is why some people make logical leaps to accept it but despite that it's still had to morph and mold to fit science/reality over the centuries it has existed.
And if you aren't, how can you say that others are? Isn't that presumptuous?