I think that the main reason Snape hates James was because he owed him his life, and because of that debt was forced to turn his back on Voldemort and the Death Eaters. Snape could have been a really powerful Dark
Wizard who commanded respect and fear and whenever he sees Harry he is reminded of how much his debt to James cost him. (Also I believe he may have loved Lily and that is another reason for him to hate Harry, because he reminds him that his worst enemy took the woman he loved.)