Meh.
While I never received physical punishment at school (I do believe it occasionally happened at my elementary school, I never got into that level of trouble there), I was occasionally spanked by my parents when I acted rotten. I don't resent my parents for it, in fact I think they're great people and love them very much. I knew at the time why I was receiving that punishment, and I'm mature enough enough now to respect them for it.
"I do not approve of running a school, or any organization, based on fear, much less the threat of physical violence." You've made a leap here that I don't think holds up. The fact that I could have received a spanking at school or that I did receive spankings at home doesn't mean either my school or my home was run "based on fear" or "the threat of physical violence." A spanking is essentially a last resort, and you know it. That's hardly "basing" anything on fear.
"We shouldn't beat children just because they're smaller than us and can't fight back." The line between basic corporal punishment of a kid who refuses to be reasonable and beating a child is a broad one. Equivocating may make your position feel superior, but it's not accurate.
That's not to say corporal punishment in the schools is a grand idea... in part because there are people out there who would enjoy hitting kids, and so screening for that kind of trait would be important. I don't get the feeling your statement was really based on any sort of reasonable accounting of those odds, though. I'd love to hear how you've arrived at your opinion regarding corporal punishment, though. It's not an unpopular one, so I don't think you're some kind of weirdo or something, I'd just be interested in knowing what kind of background you're coming from.