Well, if I listed every character in Gundam SEED that annoyed me and why, we'd be here all day, so I'll just go for the two top contenders.
First is Muruta Azrael. Man was that guy a douche. As soon as a way to cancel out the N-Jammers was discovered, instead of, I don't know, try to solve Earth's economic crisis, he tries to nuke the PLANTs, prompting ZAFT to respond in kind with the GENESIS superweapon. And during the final battle, he tried to usurp command of the ship he was on when things weren't going his way, forcing Mu, the coolest character in the show, to commit a Heroic Sacrifice. Then he shoots up Baguerile in a childish tantrum, and then gets blown up. Good riddance.
Second would of course go to Flay, for deliberately acting like a selfish bitch, and having a very annoying voice, at least as far as the dub goes. Though, she does mellow out towards the end of the series, and is partially redeemed when she gets killed off in a rather mean-spirited manner, and her ghost/spirit/hallucination/whatever apologised for being a bitch.