As is said in the books, (moreover in the Sorting Hat's song in OotP), Slytherin wasn't originally "evil," that came about after strife amongst the other teachers, who were likely also partly to blame....
Simply put, the enmity lasted over the generations.
Diamonds: It is my personal theory that Snape does have a heart
Spoiler:
- that is, that he repented in truth, and was sent begrudgingly back to work for Voldemort by Dumbledore - hence the "hatred" in his eyes when he looked upon the Headmaster at the end of HBP.