Arguing with people won't change anyone's mind. Most often, getting into an argument with someone of opposing opinion will only serve to increase conviction in your own point, at least in the short term. Most humans have a lovely stubborn streak that, when challenged, makes us hold tighter to our own arguments, even if the arguments are without fact or sense. It is easier for me to think that you are an idiot while we "discuss" the state of affairs than for me to admit to you that I am wrong. In most situations, that would be a loss of face.
However, I agree with Muke that in the long run, you may change your own mind after having mulled over the points your argument opponent has made. I know that in past, I have vigorously defended some opinion against one person, yet when faced with another person on the same topic, I have used the points made by the first person as if they were my own.
Humans are flawed. Logic is not the strong point of most people I know.