I think that the real hatred began the first time that Spike cought Anger having sex with Dru (I don't remember the Angel episode) and sort of escalated from there. Of course, as the alpha male of the vampire pack, Angel would naturally be the target of the next highest male (assuming that the vampire hierarchy runs the same way as other predators, as it seems to, given the fact that Darla, Angel's sire and therefore senior member of the pack seems to defer to "her boy" in most things). Also, while there is no direct evidence of this on the show, it has been conjectured that there might be a history of sexual abuse involving the two. Finally, there is simply the two different personalities, Angel being basicly a bully and a rapist who enjoys torturing his victims before killing them, while Spike seems more inclined to seek out what he considers more worthy opponents (i.e. Slayers and even other vampires). William probably considered himself the mental superior of Angelus, hense the "Spike" persona, more the ruffian than the poet, could have been simply an attempt to "fit in" with Angelus, at least initially.