We have grown men in Fallout acting like 12 year olds too but that isn't the point...
I can't tell you why older gamers hate kids, manly because I'm 19, I however, can tell you why I hate kids in real life.
They fuck everything, the reason we can't have nice things almost always leads to kids, of course they're passive aggressors most of the time.
Wanna take off your shirt in an open air restaurant because it's hot? You can't, it's a family restaurant.
Wanna tell dirty jokes with the guys at your table? You can't, the guy on the table next to you had the idea to bring his stupid kids to a bar.
Wanna smoke? You can't, kids.
Wanna say what you actually think to your family during christmas' eve? You can't, your younger cousins are there.
Wanna get laid on christmas? You can't, your whatever year old nephews whom you never seen will be at the tonight's family reunion so for some reason it would be bad if you didn't go to the reunion just because your nephews.
Wanna hear the ending of a really nasty story? You can't, kid walking towards your table.
You wanna play a nice mature (not pornographic, MATURE) game with no general bs you see on certain games? You can't, too many teens and kids nowadays burning their mom's credit card on games to make a truly mature game.
You wanna 'hit that" but all she can do is go "baaawww!" on some baby nearby.
You wanna have fun with the part of your family you like but there's always that mother that always needs something for her baby, and it's usually silly stuff like mashed peas or she'll choke and not have a singing voice or whatever.
I'm not saying we should stop having kids, what I'm trying to say is that children are way too much blended into human society in general, they need to build a huge school life-tutorial thing that you can't leave until you're 18 or something.
Ever since I turned 18 I've been ashamed of ever being a kid, I'm probably more ashamed of being a kid in the past than anything I did and probably will do.
I hope that helped your question, those are the best examples I can think of on why kids annoy people over 18.
TL;DR: Kids blend in with adults too much, like that lame kid in school you didn't want to talk to but he always tried to talk to you and your group.