When a child is still in the womb, he or she is entirely dependent on the mother, depending on her for protection, sustenance, and stimulation.
However, when the child is born, the process of childbirth already signals separation and also of independence. While the baby could still not fend for himself, he is already independent of his mother and is entirely new individual.
Of course, the levels of independence are based on the age and maturity of the child, but it is mostly dependent on the perception of parents. Sometimes, they are just too afraid to let go or they are just afraid of repercussions. Nevertheless, if they just give their children the chance to explore, then both parents and kids will realize independence early on in life.
While each child is different, parents will not know when a child is ready to do something if they never try at all.