Sorry, I was partially wrong and what I meant about the Slytherin thing is that he would not have even thought to call Lily a mudblood when he was embarrassed had he not been in Slytherin (just my opinion). I know Snape never saw Lily as less being muggleborn.
Calling Lily mudblood may have been the straw that broke the camels back but his will to want to become a death eater and the things he did with his Slytherin freinds with his facination for the Dark Arts really disturbed her, and this is depicted in the book of what drove Snape and Lily apart from the get go.