Why is physical abuse of a child inappropriate?
First of all, anything that is called "abuse" is by its nature inappropriate. No one would argue that physical abuse is good, but they might well argue about what constitutes physical abuse.
That said, physical abuse is bad because it makes it more likely that the abused child will have reduced life chances as he or she grows up. Children who have suffered from abuse are more likely to perform poorly in school. They are likely to act in ways that make them socially unpopular. As adolescents, they are more likely to engage in activities that get them in trouble with the juvenile justice system. When they are older, they are more likely to become depressed and to have substance abuse problems. For these reasons and that of physical injury, (putting aside reasons of morality) it is inappropriate to physically abuse children.