What's your parents reasoning for not staying out late?

Rhetorically address that reason politely, defeat all of their concerns. But you need to do this not in a permission seeking way, and not in a submissive way either. Do this to defeat their argument and quickly blow over it into a battle of wills.

Rhetorically addressing their concern for you staying out late shouldn't be a plea deal, it's almost to say "I'm going out anyway, but so you know that I'm conscious of what you're trying to say, I'll do x and not do x so that you feel better about it."

But tell them you intend on having a social, fulfilled youth, and quite frankly that you don't give a fuck about whatever reason they have for not letting you stay out late.

They need to know that it is unacceptable of them to disallow you to stay out late, there's no way in hell that you will be oppressed in this way, it's their deficiency that's causing this treatment, this is the way I intend on living my life, these are the goals I have for myself, You're either with me or against me.

You need to keep extreme pressure on, defeat them rhetorically 100 times over but don't devolve into semantics and petty arguement. Stay on topic, and take every opportunity to give a psuedo speech re-inforcing the positive aspects, highlighting the lack of negative aspects, and re-iterating how it's their deficiency that's putting a restraint on you, and that you don't intend on being restrained in this area because of how retarded their deficiency is, you understand their concerns but it has to be this way.

You need to be more powerful than them, don't be too emotionally reactive, don't be a pushover but don't be unnecessarily argumentative.