- let people finish their statement: If you don't let someone finish and you interrupt, they will decide that you are just refusing to hear them out rather than disagreeing. It doesn't matter if you can prove mathematically with extensive sources and footnotes, most of the time they won't be able to accept that you understood their point and showed it to be flawed.
- pause long enough after they speak: Again, if you instantly explain why they are wrong, most of the time other people will not be able to handle this. They will decide you didn't actually consider what they said. It doesn't matter what is actually true, and if you somehow do convince them that you are right they will be doubly resistant since you are making them feel stupid on top of everything else. A huge benefit of this and the previous bullet is that you will often find that at first you misinterpreted what the person was saying, so you were about to disagree for no reason.
- don't force them to admit to themselves that they were wrong: if you let people 'save face' they can just get on board and agree with you. If you force them to grapple with being wrong they will be difficult and will hate your guts. It may seem silly, but replying 'I don't think that will work because ...' is going to be the source of turmoil, when saying 'Interesting. Previously we did something similar to that but we had a problem where ...' is going to win the other person over instantly most of the time. Later they will see that they were wrong, but you didn't rub their nose in it and force them to grapple with it in a social setting where they are going to have to feel shame.
Failure to do these things is just what people mean whenever they say someone is arrogant.