It's clear why Snape picked on Harry (because of James); or on Hermione (Harry's friend; and ALSO a Gryffindor, AND a muggleborn, with audacity to know the subject and annoyance of showing it off when he wanted Gryffindors AND muggleborns to look stupid and incompetent).
But why would he pick on Neville so hard?
Neville wasn't Harry's friend, he wasn't a typical Snape-rubbing-raw Gryffindor, and for sure Snape wouldn't have hated him for his parents having been Aurors.
Being bad at Potions doesn't seem to be it either - otherwise he'd pick on Crabbe and Goyle more than on other Slytherins (though less than on any Gryffindors).