Two people engaged in a debate. One is challenging the opinion of the other. They go back and forth, point by point. Until it happens:
"Well, I'm entitled to my opinion."
When people say this, I think they're saying that they have the right to hold the opinion, content of the opinion notwithstanding. If so, I agree but that is basically a nonsense statement. I have the right to hop on one foot I suppose, but if someone points out that walking normally is more efficient and I, instead of engaging them on that point just say "Well, that may be but I have the right to hop on one foot" I might be right but I am also babbling and missing the point.
Address the actual content of the opinion, not your right to hold it.
That is all.