It's not a trick. There's no such thing as "being right" overall, that only exists in formal logic (i.e. in theory): https://en.wikipedia.org/wiki/Solipsism

Right or wrong is all relative to a segmentation. You don't discover who's right or wrong through debate, you discover whether you can agree or not, and why. Formal logic sidesteps this by definining a common ground up front.

I'm committed to my position, and I do think it is "right". But that doesn't necessarily mean much. Same for you. If this was more commonly understood, I think that would indeed be nice. See also the "agree to disagree" you issued up top. This is what that actually means.