It could also be that you (OP) could be wrong (at least sometimes) but continue to insist that you are correct. But consider that needing to be right is just another way of saying needing to prove other people wrong. That is exhausting and infuriating from the other side to have someone constantly tear you down. It's not being factually correct that's infuriating, it's the attitude that goes along with needing to be correctz because (if it's being pointed out to you in such a manner) it's not done in a friendly way, but an adversarial way.

People usually just want to have fun, friendly, conversations. When someone, sometimes not even the person you're talking to, butts in and keeps insisting your wrong and that you must acknowledge them, it's extremely rude. It derails the conversation to centre around how smart you (think you) are, instead of the topic, in an adversarial way.

I know someone who "had to have the last word". I'm still trying to figure out if he's maybe neurodivergent and honestly doesn't understand, or if he's just an arrogant asshole. But the end result is the same: you come off as a arrogant asshole, and no one will like you for it. Not only does he always "have to be right", he inserts himself when people aren't even talking to him, and won't let other people move on with the conversation until they acknowledge that he's right. It's rude, selfish, and self centred behaviour.

And then he cries himself the victim when people don't like him, which makes everyone dislike him even more.

The fact that you're even asking this question in this way ("how do I be right?" and not "why do people say this?") shows your need to be correct and make someone else wrong, and your victim complex about it. If I knew you in real life, I wouldn't be your friend.