I couldn't agree more with you. Sometimes you will find some one who hates you even before your birth. What can you do for that? There may hates you because your race, believe, ideas or even worse in language sites they will hates you because your languages' weak skills thinking that you may need their help. You want to know why? I think it is hard to know why. Maybe there are another reasons .  You already said "In fact, they hate themselves. But you're just a reflection of what they wish to be."

Therefor, if we want to reshape the meantioned reasons with your ideas then the following is very interesting:

Hate because:

- Race ( they have many historycal problems with races , thinking that they are better than other)

- Believe ( They have many problem with their own believe . Particulary because of the horroble past)

- Ideas ( they have very strict and narrow political ideas_ right wings or rasciest party)

- Language ( they have some problems with language skills like listening, speaking and writing)

Finally, Maybe my analysis isn't right but I feel of you because I used to be in position like yours. 

Chris, I'm glad for you that you are so indifferent, but I'm not. I don't say that I'm an ideal person. I have done a lot of bad things and there are people who have enough reasons to hate me. It's quite normal and naturally. But also there are men who hate you without any reason. And I just want to know why. 

By the way, you don't have any right to judge me. 

Hate is a strong word. Sometimes people just find other people annoying and then avoid eachother, it happens. Not the fault of the one person, nor the other. Personally I think people who think they should be liked by everyone are equally irritating. Or people that think that everybody should like everybody. That is one day a year at Christmas, and that is enough for me. 

Now what if that somebody hates you? What do you do? I probably have a total different character then you, I dont care much what people think of me, I fear. I would just dont care and ignore after an irritation period. I actually would not spend a discussion topic on it, and continue my study here. There is always somebody who dislikes you, and there is always somebody who gets on your nerves. Again nobody is to blame. It is life, move on and learn the language.

They are insecure.
They dont have self confidence and they gain confidence by  hating others.

They are not understanding od they dont have enough tolerance capacity.

Maybe they have the same personality with the person he hates or it's the other way around.

They just dont have nothing to do. If you are not a doer you are an observant and it is easy to see what u hate about a person than what u like about them.

Pupsik, I don't hate haters in reply. I just feel sorry for them.