In fairness, Snape was snide to most of his students. The only one we ever hear of him being nice to is Draco.
I think in the beginning Snape was just snide to her- mocking her for her know it all attitude- much like Ron did. She just kind of rubs some people the wrong way at first meeting.

I think as the series goes on, he sees the trio getting away with everything and dislikes all of them for it. They sneak around at all hours, break rules, have overly familiar relationships with staff (Hagrid and DD) and do things no other student has ever been able to do. He hates Harry the most because his attitude reminds him of James, but all three of them are flagrant rule breakers and prove their superiority to teachers over and over. They get past the teachers challenges protecting the stone, find the COS after all generations of teachers couldn't find it and they foil LV when so many adults tried and failed. I think he became a professor at Hogwarts to get the respect and status he could never get from his peers. Their abilities disturb his natural order.