The Suzaku hate stems from many things. He is just annoying. He is like that guy you knew from when you were little that was a massive tattletale, someone who never let you bend or break the rules, even though you could get away with it. And if you DID bend or break the rules, he would have no qualms about selling you out. Suzaku is that guy, cept all grown up and still lacking the ability to realize that the world isn't black and white. It his Suzaku's dogged adherence to the straight and narrow that is what pisses most of us off. Further, he seems blind to the fact that adhering to the straight and narrow will not get him anywhere, due to the fact that the authorities he is reporting to are the very ones who are the source of the oppression in the first place. He is, essentially, a lapdog. His loyalty has never been to himself, his friends, or his family. He always has pledged allegence to the "higher ideals" he believes in, and by proxy whomever can help them fulfill them. Case in point, he willingly killed his own father when he was younger, in an attempt to save the lives the Japanese. What ended up happening was that the Japanese were killed anyway, and those that lived on were oppressed. He then joined the oppressors rather than fighting for his own people, so that he could fight for what was "right" by respecting the governing authority of Japan, or rather, Area 11 now.
At the core of the matter is that he seems inhuman. Lelouch is selfish in his motives, he has urges and desires and ambitions and whims. Suzaku doesn't. All we've ever seen him do is follow the orders of someone else, the entire time. He is selfless to a fault, following the orders of his superiors without question. The only time we have seen him do something for himself was when he demanded a promotion in exchange for SELLING HIS FRIEND OUT. The one time he did something self motivated, it wasn't something petty, it was a deep betrayal.