Why do so many online users, obnoxiously correct your use of the words "your" and "you're"?

makes them feel smart

If you are asking in the Words and Wordplay section, they may be assume you're looking for someone to correct your errors. Not everyone does know the difference, especially if English is not their first language.

People don't know that you know the difference, because you aren't demonstrating that you know the difference. What you are demonstrating is that you in fact don't know the difference. Yes, it's a stupid mistake, so it makes whomever does it look stupid. By telling you your mistake, they are helping you to not do it again in an effort of preventing you from appearing so ignorant in future. The moment you stop accepting criticism from others is the moment you stop learning. Don't be obtuse, and don't be obstinate. Accept your mistakes, learn from them, and move on.

Why do you disrespect your readers so much that you can't even make the effort to spell correctly something that you admit you know is spelled incorrectly?

Don't try to displace the "blame" onto other people. You're the one who is deliberately making it harder for other people to read what you write.

I hope this is the biggest problem in you're life.