AoC and 'parental ownership'

I see repeated claim that age of consent laws treat children as if they were property of parents.

Utter nonsense!

AoC laws are in violation of parental ownership! If parents owned their children, they should be free to authorize their children to have sex, if the parents are so inclined.
Instead, the AoC laws punish people for sex with children regardless of the opinion of parents, and also punish parents for tolerating children who have sex.

Therefore, AoC laws treat children as property of state, not parents.

Would you prefer if children were treated as property of parents?