How do I convince someone that I'm really right...

YOu can't... debate is mostly intellectual masturbation. It is rare when a person changes their opinion in a conversation if they came to a conversation with an already formed opinion.

Club him with something that hurts. If that doesn't get him to change his mind, repeat. Eventually he will probably give in and agree with you.

One thing I tend to do in a situation like that, is take a step back and try to figure out WHY I want to convince someone? Often I learn a lot about myself (and sometimes the other party in the debate, since we're both human) just by trying to figure out my own motives for what I do, and sometimes I realise that even tho I may have been "right" my motives for wanting someone else to believe me or accept what I say as true were not always in their (or my) best interest. We ALL seem to like to believe some things that are not true, so I nowadays am more likely to let it slide than I used to be when someone doesn't agree, and just say "fine, we will have to disagree on that."

Just as you have a want or need to believe that the scientific answer is the truth (which it may be) and convince your neighbour of that, he also has some want or need to believe what he believes. To some extent, we are all perverse delusional psychopaths. We all need to believe some things that may be lies in order to function.

Of course there are limits to how far we are willing to go with "letting someone else believe what we consider a lie" - and eventually of course if there's enough strong feeling behind the disagreement it escalates in the manner Theaetetus described and you can end up with all-out war LOL - so in any disagreement you have to weigh it up and decide if convincing them is really worth the possible trouble? Sometimes it's just easier to live and let live LOL. Of course, there would seem to be times when confrontation is unavoidable or necessary, but that's a whole other debate.

So, my way of thinking in your situation (at each stage of the argument) would be: "why do I want to convince the other person" and "is it worth it?"

The great Acarya Maitreya says in his Saptadasa-bhumi-sastra-yogacarya:

"Before accepting a challenge for a debate, one should consider whether his opponent is a person worthy of carrying on debate through the process of proposition (siddhanta), reason (hetu), example (udaharana), etc. He should, before proceeding there, consider whether the debate will exercise any good influence on his opponent, the umpire, and the audience. But first of all, he should consider whether a debate - even won - would not bring him more harm than benefit."

It is only ego stroking to think that you need to convince anyone that you are correct in general conversation. You can offer the data, and your interpretation of the data, but what he does with it all is not your concern, generally.
In this case, it seems to be all ego (your emotional aspect; anger, for instance, all point at ego...).

What is it that convinces you? Show your neighbour this. It sounds like he's a wind-up artist and will still say he doesn't believe it, but then that's belief for you: it has nothing to do with knowledge, truth or intelligence.