I found this very interesting 20 page Document titled "What is Proof?" That I pulled a couple sections out of.
This article is really eye opener for me. It helps one to see that just making assertions is not proof. Just out-arguing a real or imaginary opponent does not show proof. Just because we may (seemingly) overpower another person of a differing viewpoint does not prove we are right.
When I took my daughter to weekly debate class for a couple years, I saw how the debaters had to thoroughly learn both sides of the issue. In a debate while debating a number of opponents they would be called upon to debate one side of the issue with one opponent, then they'd have to debate the other side of the issue with the next opponent. Although I wasn't actually in the debates, but only a spectator, I saw the importance of learning to see the other side rather than just the side that I may be emotionally attached to.