Do you have a licensed therapist who specialises in gender issues, who knows what gender dysphoria/dysmorphia is? Has that therapist formally diagnosed you with gender dysphoria/dysmorphia and said, "Yeah, you really should undergo medical transition so that your body matches your mind"?
You do? Ah. I see. And that's not good enough for your parents? Hmm...interesting. What if you were to get a second opinion from another mental health therapist who may not necessarily specialise in gender issues, but would definitely know gender dysphoria/dysmorphia when confronted with it? Would that be enough?
Because it honestly sounds like your parents are looking for a solid excuse to invalidate your feelings so they'll be more comfortable with who they think you are. You're not, as far as I know, a psychologist or psychiatrist, so the burden of searching for answers just to confirm what you and a professional already knows, should not lie with you. Yes, there's a chance your parents are just looking out for you and your well-being. But there's a stronger chance that they're just uncomfortable with you, or anyone else, being gender non-conformative.
I think it would be worthwhile to ask them, "Would you believe me if I got a second professional opinion?" Then follow up with some facts: that therapy costs a small fortune, and that a second opinion will pretty much bolster the first one. See how they react. Just my tuppence.