Suppose you meet someone for the first time. A way to impress them might be to talk intelligently at them for a while, reeling off a litany of impressive knowledge and reasoning. But while you might impress, you wouldn't learn much from the other person. On the other hand, you could meet that person and spend your time listening and learning, forgoing opportunities to impress them with your own conversational gifts.
Ideal conversations are probably about half and half - with both agents having roughly equal listening and talking time. While on my day I could make an impact on an interlocutor with some impressive knowledge and reasoning, I find what generally happens when I converse with a stranger is that I tend to allow the conversational output to be largely about the other person, because I want to 'soak up' as much new knowledge within that brief window as possible.
Here's why. Suppose you get chatting with a stranger and the chances are you won't get to do it again any time soon. Yes you could impress them by talking intelligently at them for a while, but equally you could use the opportunity to learn something from someone who knows more about a subject than you. Any stranger is going to have areas of knowledge that surpass yours, be it knowledge related to their job, their hobby, or simply a keen interest of study.
Consequently, then, if you and I meet as strangers, there's a good chance that I'll be highly interested in something you know about that I can add to my knowledge stock - be it plumbing a bathroom, working as a solicitor, your superior sporting talent, your experiences in a foreign country, an author you've read that I haven't, or numerous other areas of knowledge you have in which mine is less prodigious.
Being willing to soak up other people's expertise is a rewarding pursuit, and well worth resisting the temptation to predominate a conversation. And don't worry about not getting your chance to express intelligence - taking an interest in others and asking sharp and incisive questions will give exhibition to an intelligent mind at work.
For further consideration, there's another element to this. Being better informed isn't a panacea against being wrong. Given that even well informed people have faulty reasoning, it is not a good assumption to say "You are well informed therefore you're probably right". A better question to pursue would be "If I knew as much as you do on the subject, would I agree with your conclusions?". If your interlocutor says 'yes' it may show confidence that they think they can back up their position. If on the other hand they say 'no' it may well be an indication that they hold that view for different and possibly fragile reasons.
Suppose Jack and Jill disagree on five things. In four of the five cases Jack says that if Jill knew as much as he did on those subjects she would agree with him. But in the other case Jack admits that if Jill knew as much as he did on that subject she'd still disagree with him. On which of these scenarios do you trust Jack the most: on the four cases in which if Jill said 'show your work' there would be enough to convince her Jack was right; or in the one case where if Jill said 'show your work' there would not be enough to convince her Jack was right? In all probability it would be the former.
It has to be said though, there is a difference between evidence showing someone to be wrong and that person actually changing their mind. For example, it would very easy to provide the scientific evidence to show that evolution is a fact, but that doesn't mean a young earth creationist would change their mind when presented with it. It would also be very easy to provide the economic evidence that import tariffs are bad for the economy, but that doesn't mean a politician will suddenly stop supporting them. Bias and self-interest are powerful tools of motivation even in the face of contra evidence.
It's very likely is that if a person believes something that is not true, and doesn't appear very bothered about the evidence connected to showing the falsity of the belief, their reasons for believing it are motivated by very strong and influential non-empirical factors, like being part of a cult or wishing to deceive large swathes of the population. This is why in any consideration of truths and facts, open, honest, rigorous dialogue that presents evidence and the weight of arguments from both sides is always going to be the best course of action.
That is why, if anyone disagrees with me about anything, I am always enthusiastically wishing to debate openly about it, and have all the arguments from both sides laid out like a buffet on a dining table. My experience tells me that the 'buffet' standard is a pretty reliable standard for separating the genuine truth seekers from those who believe what they want to believe irrespective of truths and facts.