Most of the time a parent and his child agree about who should control something. The parent pays for the baby's food and the baby doesn't object. This is not "control" in the relevant sense because the baby prefers it be this way. And other times the baby decides on the location of his rattle. He exercises some control over his life and his parent is fine with that.
The interesting case -- and the one where the notion of an adult controlling a child is most relevant and meaningful -- is when there is a disagreement. Then if the adult, say, unplugs the TV to prevent the child playing GTA, against the child's will, he is taking control of the situation and exercising control over the child's life.
A wide variety of excuses are given for adults controlling children as a react to disagreements. One particularly generic and offensive one is "kids don't think so good". This sometimes takes more specific forms, e.g. "kids don't think so good on the specific issue of differentiating between virtual reality and reality" (btw, ironically, most adults are extremely bad at that same issue in some different forms, e.g. they don't really understand that when they "see" a chair the visual image is a VR rendering inside their head).
Anyway, here is a fact that, ahem, adults often mess up and which many young children intuitively seem to grasp: if we accept that the ratio of stuff adults are right about to stuff children are right about is 1000:1, it does not follow that in a disagreement the adult is right (or probably right). This is because disagreements do not happen in a random sample of cases. Disagreements only happen when both parties judge that they have relevant information that the other hasn't properly taken into account.
In disagreements, it's nothing but sheer unadulterated arrogance (and irrationality) to assume one is right. And to attribute this assumption to demographic characteristics of the other person is dehumanizing.