I would do the following:
1) Understand that there is either a miscommunication or a difference in values. Try to figure out what they are.
2) Next step is to make an attempt at building a bridge with the other individual.
3) If that doesn't work and if people are watching and listening, present arguments for the benefit of those people in a rational way and step aside once that's done.
4) If no one is watching and bridges can't be built, abandon the conversation immediately and move on.
My issue is that I mostly ask questions to try and understand their position. Then their entire argument starts to make less sense. So they stop answering my questions and say that what I’m doing is dumb because I’m asking questions I know the answer to. It’s like they just want to have a shouting match which I don’t engage in. But then when they start insulting, I wonder if they are stupid or just immature.
It's because people have a limited amount of time in a day and they likely wouldn't want to repeat the foundations of their position to everyone they meet.
This is why we divide sets of ideas into schools of thought so that we can build on them instead of starting from scratch. Kind of like SDK's for ideas to which we can add our own creative thinking.
Also, repeated questions in a private conversation makes sense, but in public, it can give the other person suspicion that you are doing it just to put their ideas down in front of other people, even if you do it in good faith.
