your parents are guiding you right. I can ride brakeless fine but its really a dumb thing (and fun too). It took my dad telling me he really thinks i should put a brake on to do it and I'm gonna be a junior in college (19yrs old) (even though I didn't want to). i was reluctant at 1st but am thankful i listened. it will makes things easier on you even though you probably will be capable of riding without one. who cares about the cleanness of how a bike looks, you are riding it not using it to show how "good" you are by riding brakeless. I'm not knocking anyone who rides w/o one because i too have done it and loved it but i for me i like to have as many backup as i can (if you have three ways of slowing down, why limit yourself to two? = backpedal, ted shred, brake). I think brakeless is for me since I can do it fine but chose otherwise just because I want to be safe both for me and others. also think of the long tern too. fact is it does some negativity to your knees (whether severe or minute depends on your riding style)

also its not too smart to go brakeless with your 1st fixie, especially when you need skipping and skidding in your arsenal so if you can't do these then don't do it at all.

I'm not telling you to put a brake on, i started with a brake, took it off, and put one back on and don't regret it. just think about why your parents are telling you to put one on. they love you and care for your well being. hope you choose what's best for you.