Great question, and another way to phrase this question (the one i will respond to in this answer) "is it productive to argue with people?".
It certainly can be productive to argue with people and contradict them. If you just keep going along with what someone is doing without putting up any resistance to it, they will keep doing it, and the same thing goes with unchallenged ideas.
However, in all arugments, you have to understand when the other person simply does not understand what your saying, it will feel like your butting your head into a brick wall. At that point, if you continue to argue, then you are committing the wrong/stupidity, not the other person. Generally speaking, if you start to feel frustrated, as in you can't find ways of rephrasing what your saying, then you are at this point.
There are certain things you need to watch out for when trying to convince other people of something, and this requires a lot of foresight. Sometimes it can be rediculously easy these days to make someone want to hurt you. ten cuidado