I don't feel the distinction is justified. To quote myself:
I don't understand how a young child can be developed enough to recognize the cause and effect of smacking, but not of other punishments.
I don't think the emotional impact of isolating them for a time out, in combination with you raising your voice and using aggressive body language, is that distant and abstract from the cause. If they are too young to draw this basic, virtually immediate connection, then are they old enough to be making the connection between physical violence and it's cause, and learn to change behaviour from the experience?
And the school cares for the child for 8 hours a day, most days of the year. This is more time than many parents spend with their children. A teacher has full responsibility for the safety and development of a child during this time. They have full legal and moral responsibility for what happens to the child during this time.
What responsibility do parents have that a school doesn't? Schools are always liable when something goes wrong.
I don't believe I implied such a relationship. I don't believe anybody 'belongs' to anyone else, I don't like the implications of ownership that word implies, they have relationships with other people. It depends on what you mean by 'belonging' to someone.
Why should a child respect the authority of a parent, but not others? A parent is as likely (or more) to abuse that authority as anyone else. Many parents use their authority irresponsibly and children shouldn't accept this authority.
As an adult in our society, you are expected to show respect for the authority of anyone who holds more power than you. Your employer, police, judiciary etc.. Accepting the authority of anyone in power is a more realistic lesson than just teaching them to accept parental authority.