Well, equality would be fine with me too.
But, in my experience and observation, the average man is quite content to sit around drinking, smoking and gambling. And occasionally getting up to go hunting, fishing or fighting and such. Such is the natural male condition.
While women habitually work very nearly all the time.
That's happen many time, they do both work as professional and do all hardwork things at home even the male don't even bother to wash the dishes or to whip the floor. And that's not right things to do, I think the male also should move their hand do whipping floor, cleaning the dishes, cutting the onion, helping the woman maintenance the house also.
But there something that woman have that can't be substitute to male, they might can imitate it but they never can replaces it, like being a mother for a child, and so otherwise, here they have their own role.
As the biological difference is not an alienated variable that have no effects to other variable, it do effects other variable that make both of them have it meaning and function. The things is we must put it to the proper places to make it work.
As for punishing children, I don't see that as a good idea at all. Once you've let a child develop to the stage where corporal punishment (if that's what you mean) is necessary, you've already lost the struggle to bring them up in a civilized manner.
Then, all you're doing is demonstrating that violence is an effective way to solve conflict. Bad idea.
Punishment it doesn't have to be corporal punishment but punishment is needed in my opinion. As a person I do believe in moral and ethics, to develop the feeling of guilt in the child who later to be their inner control in life that construct them to have a strong principal and view of right or wrong punishment is something needed but not the central.
For example, one of my friends is a vice principal of one of modern elementary school which the school were regulated with total communication and there are no punishment and compulsion even in a very light form. Teacher are work as total facilitator not as a dominant and controller educator.
But there also lack from this system. As they also mostly the children are come from rich family, even in Intelligence they are superior because the school method able to increase their curiosity in learning, reading also boost their creativity. But in moral and ethical aspect most of them were very low. They can call their teacher "dog" if they angry, and hitting their baby sitter, act aggressively if something going out from their expectation. In short, they grow to be a spoil kid who have no border and this becoming an issue in that school.
Having a children mean leadership, you too harsh and press them, they are unproductive or rebelling, you are to soft they becoming spoil and you break their character.
The combination of it, it is the best. The best way always the middle way, not extreme left, not extreme right, but just, right into the center.