I actually don't think that Seifer and Squall hated each other. Seifer was trying to follow his dreams, and Squall was perceived as an obstacle to him. Squall himself only went against Seifer because he was the obstacle to the Sorceress, the primary part of his mission.
I'm not saying that two were "buddy-buddy", but they didn't hate each other; in fact they respected each other very much
