My Opinion Isn't (A) Right

After reading and discussing "Right to Your Opinion" all I can say is wow. It's astonishing how much controversy one piece can cause. For me, the main problem is the exact words "everyone is entitled to their own opinion". Yes I 100% agree that everyone can have their own opinion but when you say someone is entitled to it, you're saying that they have a legal right and when they have a right, everyone has a duty to what? Respect it? Believe it? People say this all the time in arguments. When people say "I'm entitled to my own opinion" and expect that to be the "winning" line in the argument, they're wrong. That doesn't even make sense. You have your own opinion on something, good for you; that doesn't mean anything. You have to have evidence to support what you say. People think that their opinions are sacred and when confronted with a counterargument, they automatically become offended. They don't even consider that fact that they may actually be wrong. When people say that they're entitled to their opinion in an argument, it prohibits them from changing their mind or being open to other views. I completely agree that everyone can have their own opinion on things, but with that said, I also believe that they must respect other people's opinions as well.