Yes. Adulthood is the time when parents become friends with their child, but as you say they will always be the parents 'child', and the hardest thing is to be confident you have done the best you can and leave them to make their own mistakes. Not always easy when you can see they are going wrong and give advice they won't listen too. :)

I see so many parents trying to be 'best friends' to young children and that is not the stage to do it. They have friends their own age, they need the parent to BE a parent and that requires discipline, boundaries, and guidance.

Still, even with the best intent people screw up, but if you've done a halfway good job they recognize you did the best you could and see you as a fellow human and friend when they reach adulthood, rather than an infallible being who can fix all their mistakes. And then one day the parent may become the 'child' when they get old and frail, and the child takes the responsibility to protect and care for the vulnerable parent.

My heart breaks for those who do not have good upbringings. I'll never understand parents who subject their children to a living hell. I guess it's a testament to their character if they can survive that without becoming too screwed up.