Life does not have to involve either ruling or being ruled. Instead, we can stand side by side with no one ruling, all of us free to be in control of our own life, solving problems individually and jointly, and having fun doing so.
That parents have obligations to their children that their children do not have to them is not because children are lesser humans. It is because we parents have freely chosen to place our children in the positions they are in, living with us instead of having been adopted at birth, say. It is we parents who have the obligations to our children, not our children who have obligations to us.
The slight asymmetry is because the parent has chosen to put the child in the situation in which the child finds herself, whereas the child has not chosen to be in that situation or to put the parent in the situation.
What a moral person would do, and want, depends, among other things, on what he believes the rights of the various people concerned are. And the consistency of this moral background, helps the parties to interact with each other non-coercively.
Does financial supporting our children mean they must obey us? Is it right to expect quid pro quo for our support?