Frail Appetite
Must you try to prove that you're goth to anyone? I don't think she;s trying to prover her gothieness at all. However, she is trying to make her friend realize that most of the negative sterotypes about goths are inaccurate.
Anyways, on to sorinchako's problem!
I wouldn't suggust that you get overly defensive about your position, nor get up in C's face. Perhaps the issue would be best if let be.
However, if you do want to try to get rid of her miscinceptions, then bring the issue up casually in conversation, and try to convince her that her ideas about what goth is happen to be misguided. Perhaps give her glimpses of gothic culture... the diverse music, the amazing fashions, gothic literature from Hawthorne,Poe, Radcliffe, and others, etc.