The kind of anime fans I hate:

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People who like Chobits.
People who don't know the difference between protips and spoilers.
People who use the phrase "the manga is better than the anime."
People who make anime recommendations based on their own personal taste.
People who zealously rant on already over popular anime.
People who just don't "get it" when it comes to breaking down anime in terms of character archetypes and basic plot devices.
People who make bogus and outragous claims such as "best anime ever" or "great art combined with epic cgi and mind-blowing plot makes it beautiful and awesome" (got that one from 420chan).
People who make out-of-league recommendations to people with little to no anime experience. Some examples includes suggesting Lucky Star to someone who doesn't watch anime or recommending SZS to someone who only watches shonens. This probably falls under the personal taste category as mentioned earlier but this needs to be emphasized.
People who do anime reviews on blogs and youtube.
People who think their taste in anime is superior and ram it down other people's throats.
People who get hellbent over proper terminology (e.g. crying when someone calls a visual novel a game or anime a cartoon).

That covers some of the more annoying ones. Feel free to make your own list.