The proof is no two men experience the same thing the same way and think the same about it. Our civilization is built on the enshrinement of plurality in the political community. You shouldn't not understand this. Though it is a good exercise to reaffirm principles by argument.

You're talking about factual truth, objective reality. There can only be one factual truth. It is stupid to deny since reality confronts us with its truth whether we will it or not (hence why it inherently is totalitarian, logic being authoritarian), and that renders this truth scientifically discoverable, after which it can be established as fact.

But we can also speak of metaphysical truths, e.g. values, beliefs, religions. Factual opinion is really only presumption and conjecture about reality. Opinion properly speaking is perspectival. Thus it can only be called false if spoken dishonestly, and then it is not the opinion which is false but the person expressing it.