I totally agree with FloridaCurly - enlisting an adult friend who supports you, regardless of their own hair type, will help. Some adults have a real problem listening to those they perceive to be children.

Another good tactic for resolving stuff like this is to talk about it when it ISN'T an issue; the logic here is that if your parents are already upset about your hair, that's not the most productive time to then talk about your hair.

Try approaching just one or the other (I'd go with mom, but it depends on your relationship with them) when there's been absolutely no hair talk that day (or no fights, etc.) and ask if you can sit down for a talk.

I would also try starting with non-hair-related stuff that's very positive about yourself ("I..." statements!), like "I want to talk about my self-confidence. It's important to me that I feel good about myself, and I have been feeling really good about how I look lately..." Then introduce the idea that the reason you feel GOOD about yourself is that you're accepting your hair the way it is. Let the parent know that you love them, and you need their support to help you feel good about yourself, too. ("I love you and I respect your opinion because you're my mom, so it is important to me to have you support my choice to wear my hair naturally, even if it doesn't look like yours." or something similar). Let them know you aren't fighting them just because you think they're wrong, but because you are trying to gain their respect for your position.

I'd avoid stuff like "I'm almost 18 so... etc." or other things that play into the age factor. Just try to make it about love and support. Maybe suggest to your mom that the two of you go to a hair salon together and get a cut that makes your curly hair easier to deal with. If you can find a good salon where you live, the stylist could maybe help your mom (or dad, just stereotyping here) understand your hair a bit better. Hearing the stylist say "Wow, what great curls!" could mean a lot! This forum has a good section for finding a stylist.

Good luck, and way to go!
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I'm mostly away doing field work through mid-May.

Hair: curlybob, fine, dense, low-po, big waves/ringlets (2C/3A)
Co-Wash: Nature's Gate Herbal Conditioner
RO: YTC Carrot, Aubrey Organics GPB
LI: BS Shea Soft Styling Cream (HG)
Styling: KCCC, Garnier P&C Gel
1xWeek: low-poo, gelatin PT or Joico K-Pak
Hair Likes: aloe, coconut oil, humidity, protein, long walks on the beach