Well I think that's pretty easy.
Kate Hate started around Season 3 (at the latest, there was plenty of reason to start hating on her beginning with Season one's "Whatever the Case May Be" with her erratic behavior) when she started bouncing back and forth between Jack and Sawyer based on whatever whim struck her fancy that day. She seemed like a petulant child who didn't make any sense beginning in the middle of season 1 and it only got worse as the seasons progressed. There's really not much to like about Kate past the mid-point in Season one.
Jack Hate started because he's so stubbornly retarded to the obvious; something special is happening on the island. It's a place of wonders and miracles obviously and yet when the island disappears in front of him, he's still in denial. He's started to redeem himself somewhat this year with his acting on faith and acceptance of the island and his destiny, but for 5 seasons, he's an oblivious moron who can't face the truth.
Sawyer love should be obvious. He's the witty, flawed and the charismatic rascal everybody initially loves to hate but gradually redeems himself by reaching out to his fellow castaways and eventually even taking leadership in later seasons, most notably Season 5 as LaFluer. He's the tragic character whom everyone has a little sympathy since he lost his parents when he was a child and has struggled with his whole life.
