They needed the seats to move their staff operationally. To do that, they needed some passengers to volunteer to not fly. To do so, they needed to offer incentives, not demands.
The airline's problem is that they didn't want to pay enough. So they used force, not only that, they used public security (police) to enforce a private contractual matter (not providing travel, even though the passenger was in complete contractual compliance).
The security staff were briefed, and if not, should have waited until they were. He wasn't "acting strange", he was upset at not travelling as he had paid for, and wasn't been offered a reasonable alternative.
Excusing this behavior is allowing it to continue.
I would also suggest considering that e.g. bus drivers face noncompliant passengers (non-paying, even!) far more frequently, and they have pretty good peaceful means of dealing with them.
Clearly it was adjudicated that it was excessive in this United instance by people qualified and knowledgeable of all the factors but that doesn't override that fundamental point that when force is used then injuries are possible and probable.
Sure it does. Because force isn't binary, which circles us back directly to where I made this point above. Your logic only makes sense if you treat "force" as binary.
I already answered your question about the degree of force in that I don't know, and that "people qualified and knowledgeable of all the factors" have already decided for this particular instance that it was excessive.
Now you're just using ad hominem to make your point.
The security staff is charged with removing someone from an aircraft, without knowing their intentions, who's already acting strange by refusing to leave in the first place, and acting in limited space with lots of other people around. They could've done a better job, but it also could've been much worse.