I see two points of view here.
Your parents want what is best for you, and you are a rebelling teenager who challenges your parents. There is nothing wrong with either of these things.
Now when it comes to religion, i understand where you are coming from. I believe that it is the soul which we should purify but still keep our bodies in health and look after them as they have been given from the akal purakh. However, the body houses the soul, and the body is cremated after death, it is the soul which "lives" on.
Being part of a religion and religious, in my opinion requires understanding as much as it requires faith. You need to understand WHY it is not allowed for a Sikh to cut their hair and WHAT it symbolises. You can listen to both sides of the arguement but until it becomes clear to you, WHY you are keeping it, i see no point in keeping your hair if it is not what you wish.
I see people who become sikhs later in their lives, especially those not born in Sikh families, and they understand, they fully engage in the religion whole heartedly and then make their commitments.
Until the day you do this, you will never see the reason behind keeping your hair and you will always question it. Once you have found the answer, and it is true to you (that is it works for you) the you will accept what is so and become committed to Sikhi.
Life is a process of remembering who we are, of remembering that we are all one with each other and one with Waheguru. Take the time to listen to what your heart says. Take time to read the Guru Granth Sahib, talk to people and see their opinions, and never fear to ask WHY. It is by asking you will understand and as i have said once you see why, once you fall in love with Sikhi, with the Lord or whatever path it is you choose, you will be 100% committed.
Good luck to you, whatever you decide to do.
Sending Light, Love and Peace to you