From birth to death, people are influenced by everything and everyone they encounter. The earlier an influence occurs, the greater the shadow it casts over every subsequent experience. The best that a parent can do is to try to give a child a useful framework to allow her to adapt and deal with those experiences on her own.
To survive, people will and must adapt to whatever is around them. That’s what learning is. Learning changes a person. And the thing about learning is that it can’t happen in a vacuum. Each of us is born with just two eyes, yet to understand a thing you need to see it from all angles. To expand one’s perspective, one needs to consult with other people; compare and contrast views, to try to find the fullest and clearest picture.
The more perspectives that you take in, strip down, and fit into the puzzle, the greater that your own becomes. If you take the view that your perspective is who you are, then as it grows, so do you.
Without the benefit of interacting with others, sharing one’s experiences, listing to theirs, arguing, butting heads, and verifying the boundaries of one’s world, a person has no chance to build her own identity — the complex, faceted lens which will allow her to survive in a complex, faceted world. Rather, she will live out her life as an avatar of her formative experiences, attempting to kludge every situation with the same hammer, unable to distinguish one dimension from another. It would be like setting Dig Dug free in the world of Grand Theft Auto.
He’s a 2D character armed with a tire pump. He’s going to keep walking to the right, and won’t even know to turn his head when crossing the street.
Assuming one has the opportunity, the weight of one’s experiences, and therefore influences, will occur far outside the influence of one’s parents. It’s the job of one’s parents to provide the resources to make the most of those experiences. It’s the job of the child to actually have them.