This one really depends on your parents. They could have many reasons for holding you so closely, so this advice may not always work.
Parents usually go through a very protective stage at some point when their kids hit their teens. Usually it happens near the end of high school but it can happen earlier or later. You have to try to understand your parents’ perspective. The baby that they brought into this world is ready to move on and they are afraid of losing you. As hard as it may get and as irrational as they may become, it is important to be gentle with your parents. Remind them that they knew this day would come eventually and that it doesn’t mean you don’t love them anymore. It merely means that you are growing up and do not depend them as much as you used to.
Tell them they should be proud that they have gotten you to this point, because they have raised you to be a responsible and mature adult who does not have to depend on others for everything. Let them know that you are the same person you have always been and that you still love them as much as you always have, you’re just ready to be more responsible and do more things and spend time with people other than mom and dad. They aren’t really losing you, just letting go of you a little. For years they have spent time teaching you. Now, they need to learn to trust what they have taught you, allow you to go out into the world with what you have been taught and learn some of life’s lessons, that can only be taught by experience.