"I haven't seen all the videos - I've only caught a glimpse of one playing on one of the cable networks. But let's assume that everything you describe happen - that she told the teacher and the administrator to fuck off, and that the cop came in and tried to get her to comply. And? Does this mean that the cop handled the situation appropriately from that point on?"
That is debatable. While I may not have handled it that way, I don't believe his choice was over the top. She removed many options by her actions
Let's look at a clip, shall we?

Notice how he tries to grab her: he puts his arm from behind her head and around her throat. How would you expect most people to react to this? What's your reaction if someone were to do it to you? You say he's trying to extricate her, by "lifting her out" of the chair and that's why he grabs her leg. But the video shows that if that was his plan it was a poorly thought out one because it's literally impossible to quickly and efficiently extricate a person from the type of desk she's sitting at with the move he's trying to perform - the desk surface gets in the way and the body isn't a floppy rag doll on account of having bones. So when that extrication attempt - if you can call it that- predictably fails, he resorts to that "plan B" you mention: flipping the entire chair back. Again, the video is illuminating: remember that his hand is around her neck, so he uses it to yank her backwards, while at the same time lifting the bottom of the chair. The result is predictable: the chair lifts and rotates backwards. The girl - her head, neck and upper torso completely unprotected - slams against the floor hard. Her legs, trapped in the desk continue moving backwards, and almost hit the student behind her in the process, as the cop finally succeeds in separating the girl from the desk by dragging her away.
You say his choice wasn't over the top. I'm curious, what would have been? Would punching her in the face be over the top? Tasing her? Ordering her to stand up at gunpoint?
We don't expect people to go limp. We do expect them to stop resisting, but are prepared for the chance they won't in most cases.
Ah, yes... "stop resisting". The war cry of the American cop.
As far as violently overcoming resistance, you can call it violent, explosive etc.
I call a spade a spade. I understand that violence is sometimes required in your line of word. But I don't think that means we should use euphemisms to sugarcoat it or differentiate between cop violence and robber violence. Doing so is dangerous.
There is a chance, had he went about it gently, and wrestled with her in the chair for several minutes, she may tire, and give up and all is resolved. The is also a good chance it escalates into her eye gouging him or biting his nose off.. in which case we would all be watching the video saying "Look at that stupid cop..."
Sure, there's a chance. Of course, there's
also a chance that she wouldn't have done any of those things you describe. It's a dangerous route to use "there's a chance that..." as a justification for this sort of thing. Mulling pulling someone over? Better PIT them instead - there's a chance they'd try to run and hit someone else. Chasing a suspect on foot? Better shoot his from behind and end the chase - there's a chance you could trip and fall.
You are right, we do need to evaluate use of force incidents, and many departments have a system in place where every single use of force is reviewed. I think its a good thing. I would recommend the officer, barring no other issues, receive additional training in dealing with these type of situations. But I don't believe based on the information at hand, I would advocate firing him.
I have no opinion on whether he should be fired or not. But I will say that having watched this video - and going only by the video - I don't think he has the temperament to be a cop. And I think you'll agree that one's temperament is very important in your line of work.