Of course people are perfectly capable of being wrong about something and saying it's their opinion doesn't change that. However, it's often difficult to tell what the truth of a situation is. You may think someone else is wrong when they're not. Therefore any given person telling you that you're wrong isn't necessarily an indicator that you're wrong or that they have better sources than you.

Even if you are right, that doesn't necessarily mean you're convincing. Even if you're convincing that doesn't necessarily mean that you've presented a justifiable argument. Even if you've presented a convincing and justifiable argument they may disagree with you. Not everyone is convinced by the same arguments, and sometimes even an argument that seems convincing can be defeated by a more strongly held sense of knowing the truth, whatever that's derived from.

There are a couple other things around this concept that I think are also important to address, because they come up a lot. Not agreeing with someone once you've heard their argument is not the same as not understanding that argument. I'd say that we'd be almost universally better off attempting to determine why it is we disagree than simply insisting that our perspective is true and trying to prove this. Otherwise, how will we ever know if the other person has a piece of the puzzle that we're missing?

Unless we're so arrogant as to assume that we know everything, in which case we most assuredly know nothing of significant value, we shouldn't jump to the assumption that disagreement means the other person is wrong, we should use it to investigate the accuracy of our own perspectives. Sometimes we're clearly right (though bias can seem quite clear), in which case the best we can do is offer a learning opportunity. This is unlikely to be achieved without being willing to understand the perspective of the person who is lacking or rejecting information. It certainly won't be done by waving away their perspective as if it didn't exist.

None of us are the arbiters of truth, but none of us are the arbiters of truth.