It's not just Teemo himself, but the kind of playerbase he attracts and that use him. Not only is his kit one of the most annoying and anti-fun-for-everyone-else in the game, but the people who play him are also often among the most annoying people who play the game.
He is next to useless in the current meta, and is only passable top. Regardless of this fact, players like to try to take him instead of a carry or support. The people who play him are generally not very good at the game and are attracted to his easy play style. Every ability he has is annoying Blind is annoying, his W allows him to run away. His E makes his low level harass ridiculous. And soon after he gets level 6 the entire map is covered in a slow/Poison.
Overall he doesn't help the team his is on, and annoys the enemy team.
It is all in people's heads. Even in games where I am the friendliest person on Earth to both teams, go top and build AP and get a tremendously positive score, people still don't honor me and like to talk down. Then I will go and play some other champ, do horrible, be rude and get honor from my team and the enemy team. It makes no sense, but people just like to hate Teemo for no reason.
Honestly, I think it is an adolescence thing. Teens like to hate things that are associated with childishness, such as things that are cute or cuddly. Teemo is very much both, and so insecure people like to hate on him just for that. Yes, his kit can be annoying, but there are about 10 other champs in this game with kits JUST as annoying as his.
Now Nunu... HE has an annoying look to him. His smug face is just begging to meet a fist.
Because he's ****ing annoying and Teemo players are obnoxious?
This part the most. They FLOCK to him.
People like to assume things about anonymous people online. Whatever people think about players is probably projected from both their own subconscious feelings about other people in general, as well as the personality of the champions themselves. Teemo is considered "annoying" (he really isn't), so people automatically project that view onto the players as well. People will believe what they want to believe.