I had a similar experience with my parents. I don't know the reason why your parents against you taking antidepressants, on my case they just said I don't need them, my situation is not that serious.
My mom is a psychologist (she even teaches children psychology to future teachers) and she couldn't notice I had depression. Only after I told her I attempted suicide at 13 she realized how bad my mental state was (that was late teens). I only took them to stabilize the chemical balance in my brain and slowly took them of. Now I'm off of them for years and feel much better, I doubt I could be that good if I wasn't taking them.
Why are your parents against the antidepressants?