Ah, Snape—he's so scary and mean to the Gryffindors, but we have a soft spot for the grump (or maybe it's just for the late Alan Rickman…hard to say). But anyway, as in the rest of the series, there's no love lost between Snape and Harry.
Snape basically thinks that Harry is an arrogant rule-breaking hooligan—and, when stuff starts going missing from his potion stash, he (thinks he) knows whom to blame:
SNAPE: Potter! What's your hurry? Congratulations, your performance in the Black Lake was inspiring. Gillyweed, am l correct?
HARRY: Yes, sir.
SNAPE: Ingenious. A rather rare herb, Gillyweed. Not something found in your everyday garden. Nor is this. Know what it is?
HARRY: Bubble juice, sir?
SNAPE: Veritaserum. Three drops of this and You-Know-Who himself would spill his darkest secrets. The use of it on a student is, regrettably, forbidden. However, should you ever steal from my personal stores again, my hand might just slip over your morning pumpkin juice.
HARRY: I haven't stolen anything.
SNAPE: Don't lie to me. Gillyweed may be innocuous, but boomslang skin? Lacewing flies? You and your little friends are brewing Polyjuice Potion, and believe me, I'm going to find out why!
Snape used to be a Death Eater, but as we learn in Dumbledore's flashback via the Pensieve, the Hogwarts headmaster swears in front of a wizarding tribunal that Snape is absolutely trustworthy:
DUMBLEDORE: As the council is very much aware, I've given evidence on this matter. Severus Snape was indeed a Death Eater and, prior to Lord Voldemort's downfall, turned spy for us at great personal risk…today he's no more a Death Eater than I am.
We as viewers, however, might need a little more convincing. He just hates Harry so much.