It wasn't Snape's choice to humiliate Hermione publicly — that was Dumbledore's decision, making use of Snape's "evil potions master" persona. Note that none of the other professors speak up, except for Quirrell, who is a temporary hire and need not follow Dumbledore's direction. Minerva doesn't even show up, presumably so that she doesn't have to sit and keep her mouth shut.

Dumbledore explains to Harry in chapter 77 that Hermione had to be seen to lose publicly in order to de-escalate the conflict with Slytherin. Dumbledore doesn't actually know that Snape was involved in escalating the conflict.

I'm still not sure why Snape wanted to escalate conflict between the bullies and SPHEW, but regardless, we can't look at his humiliation of Hermione as any evidence of his motives, because it's not actually his move.

Snape's been acting as Hermione's protector, not as her adversary. (And without telling Dumbledore about it!)

From Chapter 72:

Jaime Astorga, seventh-year of Slytherin, and until recently considered a promising upstart on the youth dueling circuit, stood ramrod straight in Professor Snape's office, with his teeth clenched tight and sweat trickling down his spine.

"I distinctly recall," said the Head of his House in a sardonic drawl, "that I warned you, and a number of others this very morning, that there were certain first-year girls who might prove annoying, if a fighter were incautious and allowed himself to be taken by surprise."

Professor Snape stalked in a slow circle around him.

"I -" said Jaime, as more sweat beaded on his forehead. He knew how ridiculous it sounded, how much of a pathetic excuse. "Sir, they shouldn't have been able to -" One first-year-girl shouldn't have been able to break his Protego, no matter what sort of ancient Charm she used - Greengrass must have had help -

But it was very clear that his Head of House wouldn't believe that.

"Oh, I quite agree," murmured Snape in a low tone, instinct with menace. "They shouldn't have. I begin to wonder if Mr. Malfoy, whatever his plotting, has a point, Astorga. It cannot be good for the repute of Slytherin's House if our fighters, rather than demonstrating their strength, lose to little girls!" Snape's voice had risen. "It is well that you had the good taste to be defeated by a little girl who is a fellow Slytherin of a Noble House, Astorga, or I would deduct points from you myself!"

Jaime Astorga's fists clenched at his side, but he couldn't think of a thing to say.

It was some time before Jaime Astorga was allowed to leave the presence of his Head of House.

And afterward, only the walls, the floor, and the ceiling saw Severus Snape's smile.

From Chapter 74:

The wands around the perimeter aimed again, low enough that their enemies wouldn't hit each other if they missed.

And then another male voice, with a similar buzz accompanying it, suddenly said "Homenum Revelio!"

An instant later there was another massive volley of shieldbreakers and hexes, fired on reflex at the suddenly revealed figure, shattering the shields which had almost immediately begun to form around it -

And then, as that same figure fell to the ground, a stunned silence.

"Professor Snape?" said the second voice. "He's the one who's been interfering?"

It was the Potions Master of Hogwarts who now lay unconscious on the stone floor, the dirt-spotted robes stirring for a final moment before they settled in place, his fallen hand outstretched toward where his wand was slowly rolling away.

"No," said the first male voice, now sounding a bit more uncertain. Then it rallied, "No, that can't possibly be it. He heard us passing the word, of course, and came along to make sure nobody screwed it up again. We'll wake him up afterward and apologize and he'll Memory-Charm the children so they don't remember, he's a Professor so he can do that. Anyway, we should make sure we're really alone now. Veritas Oculum!"