Your children are free thinkers and are their own people. Not another version of who you even while they may look very much like you.
You hope to raise them the best that you can with what you have and the will you possess inside you. You do not look down upon them because they make bad decisions. You lend a hand or wait until the lesson has been learned. When your son or daughter picks themselves up and dusts themselves off with or without help, you are proud. The parent watches and learns from the child as the child watched and learned from the parent. Trust that you were a good example.
As a parent you want to protect your children forever but you know that you will not be able to that. So you equip them with morals and reasoning. Always making sure that they know you support them unconditionally. Should they ever need your help, they know as children and as adults that your arms will be there to comfort, not to ridicule or shame.
One day that adult child of yours will look for comfort and reassurance in the arms and advice of someone else, a spouse. This person will become one of the most influential people in your child's life. You will have to let this wash over you and separate yourself from certain roles you previously filled. When you are gone, your grown child will have a family of their own and this one person to confide in. You should be proud.