Absolutely he deserved to be fired. It was stupid and unnecessarily violent, and more than that, it was an embarrassment.
Security should have known proper restraints/escort techniques. What's more important yet is not giving an unruly student extra attention - you take care of this quickly and quietly with as little spectacle as possible. Violently wrestling a small girl to the ground? You definitely lost the power struggle. It shouldn't have even gotten to this point in the first place, but a better escort technique would be for two security people to each take one arm. At first, a warning of "Are you going to be able to walk by yourself or will you need to be escorted?" with both security officers there, and if that doesn't work, a safe, painless, quiet and quick escort out of the classroom. But again, this sort of escort should be last case. Better options would be to finish class and make the girl stay behind, possibly with a security officer standing next to her for the remainder (thus, she gets no extra attention and class isn't disrupted), or hell, even have all the other students move to a different classroom or go outside for class.
Teens are not becoming "more" disrespectful. There is more media attention on their actions, however. What I am amazed by is so much cowing before police brutality and justification of it. No, it didn't matter what the girl was doing. Short of her being violent herself and threatening someone else, which might create a need for quicker action, there was no need for a violent escort. Police brutality is not okay. Police brutality is especially not okay when someone is just sitting there quietly, not harming anyone, and it does not matter how "disrespectful" she was.
Hopefully this opens a dialogue, and if teachers need better classroom management techniques, extra training for that, and certainly more rules and training in place for these security officers.