Self-respect & being right are the two important things in everyone's life. If you do not have self-respect, there is no way you can be happy in the first place. Everyone wants to be right most of the time, in fact, all of the time. You get frustrated when others don't agree with your opinions. So, what's the important for you?
It is a very difficult question though. I will choose Self Respect over being Right. Self Respect is the most valuable thing for me.