Alright, I need to really clear some thing up.
For those who don't know (apparently most of you) "Emo" can mean many things. Such as:
A. ORIGINALLY, the term referred to what was mostly an clothing style. It was an offshoot of punk, based mostly around simply wearing whatever the hell you felt like wearing. People who chose to be "emo" tended to be more in touch with their emotions than others, and NOT JUST SADNESS. They'd react more noticeably with sadness, happiness, love, anger, everything. As for the clothing, the 'rules' were almost nonexistent, and much of it could be even fluorescent and eccentric, as opposed to the bland blackness we think of today.
B. People use the word to refer to people who are seriously, legitimately, diagnostically depressed. These people really need help and compassion to be guided through their dark times and avoid leaning towards drastic measures, like committing suicide. I don't see why anyone could really hate these people, as they are usually fairly quiet, and sometimes put on a façade and don't even seem depressed to others.
C. The most common perception, the ones that are actually the most hated. These are the people that are simply attention-seekers; they simply pretend to be depressed and slouch around town looking at the ground, wearing all black and listening to MCR or something. They are the ones who deserve a good sock to the head. They are all narcissistic SOBs (or Bs, as the case may be) who simply want other peoples reaction, whether it's pity or disdain. They feed on the responses of others, similarly to internet trolls. THEY are the annoying, whiny, fake brats that we all love to hate.
D. There is sort of a fourth group. There are some people who do not act as anything remotely connected to Emo, and simply like the clothing and/or music. These ones are a test in judgment, proving that you should not see someone's clothing and hate them for the personality that you assume they have.
I, frankly, hate group C with all my heart, but all the others I have no problem with. I actually like a lot of music that is sometimes considered "Emo", such as Billy Talent and 30 Seconds To Mars. As for conformity, only group A would really have a thing against conformity. Group D is conforming themselves, and C is the DEFINITION of conformity.
"Cutters" could be different things, depending on why they do it and if they actually do. They could be group Bs who are indecisive about suicide, or group Cs who do it because they're 'supposed to'. Or even addicts to the rush it gives you.
Those who do nothing to solve their problems are likely group Bs, who don't because they are depressed (which IS A MENTAL DISORDER, PEOPLE) and lack the energy or will to do anything at all, or again, Cs who don't do anything because they don't actually have a problem.
And Emo has ABSOLUTELY NO CONNECTION TO GOTH WHATSOEVER. Goths are people who believe in and sometimes worship the unholy spirits of the damned. If anything it's closer to a religion than a style. The word 'Goth' has been mangled so much that now anyone wearing black anything is in danger of being called it, or Emo. I once got called Goth for wearing brown cargo shorts and a black XKCD t-shirt that clearly depicted a stick figure with a beaker and calculator shouting "STAND BACK, I'M GOING TO TRY SCIENCE". Labeling itself is stupid, but it only gets worse when people label incorrectly.
As for the actual question, I hate Emos (group C, that is) because they don't care about anyone but themselves. Plus they're whiny and annoying.
TL;DR: there are a lot of people that fit the "Emo" label, but the ones that do it for attention are little annoying pricks. People who cut have different reasons, Those who do nothing could have the disorder that is depression, and Goth =/= Emo AT ALL.
Sorry for having a massive post, but people who generalize Emos into one category are a pet peeve of mine.