I can understand your being upset by some of the remarks, because no one likes to feel as if one’s experience, input, ideas, etc. aren’t taken seriously. And it’s true that most of those “arguments” are nothing more than put-downs, and on that basis rude.
But the facts are that:
– You are young;
– You are inexperienced;
– You are (apparently) charming and amusing, maybe somewhat naive (that’s not a put-down);
– You are (apparently) a young American woman.
So what? They’ve pointed out the obvious. If you want to prove them wrong, then do that with results on the ground. Don’t expect that someone with more age, experience, knowledge, from another part of the world, a different culture, perhaps, will simply take your word for something that they believe they know better than you. Just acknowledge the end of the debate and move on.
The only “argument” given to you there that may have any validity is “I don’t have time for this right now.” You should acknowledge that gracefully.
For one thing, you might also recognize that a refusal to acknowledge the superiority of your idea simply because of your age, experience, gravity, culture or gender is a form of logical fallacy, a sort of ad hominem argument that the person may be relying upon to extricate themselves from an unwinnable debate. You can’t correct their manners or their world view until you “win the argument” by proving yourself right. In these cases, only time and experience will do that.
And keep in mind that unless you have absolutely certain knowledge that the other person doesn’t have, apart from “being certain” or “feeling that you just have to be right”, which is nowhere near as certain as many seem to think, your argument may also be wrong, and you just haven’t learned that yourself, yet.
Personally, I would ask the person to correct my facts when they had more time, and request that in future debates they not rely upon ad hominem arguments to dismiss your valid points. Keep the communication channels open, and you may learn something. You don’t know everything yet. No one else does, either, or ever did or will.