Hair is very culturally important, particularly for women. Very, very rarely will you see women choosing baldness as a hairstyle.
So when a woman loses her hair due to something outside her control, she suffers in our society in a number of ways.
Men don't have this issue so much because many men, particularly older men, choose to be bald, and they still appear male and attractive. Women who go bald not only lose their hair, but in our society lose a significant portion of their femininity and attractiveness.
It's hard for a man to ever know what it means for a women to lose her hair.
It's hard for women who have not lost their hair to know what a woman goes through when she does lose her hair.
I think it's great that your sisters are willing to face the public without hair so they can, in some very small part, experience a little of the pain your mother is going through.
Even if you did shave your head, you would suffer few to no consequences. At most people would ask you why the change, and you'd be forced to share the news of your family's medical problem.
However, I suspect your sisters aren't just trying to force you to show solidarity with mom - they are looking for support for them as well in their endeavor to experience hairlessness with their mother.
I know you feel like you are being forced into this without consent, and it's the unilateral nature of the situation which is most galling.
But it's just hair.
Your mother is going through a harrowing experience. Your sisters are trying to cope, and are willing to go into society completely shorn.
You don't elucidate your other reasons, but were it me I'd attach a much larger importance to my family relationships than my physical beauty (or lack thereof, in my case). It doesn't have to be meaningful to you. It's a very small way to help them deal with a terrifying disease.
Them knowing how important your hair is to you would only make your contribution more meaningful in their eyes.
Shave. Take a picture. Tell them you plan on letting it grow out with the expectation that mom will be in remission before you get back to your current hairstyle. They probably won't insist on you continuing to shave your head.
Don't be stubborn over this. It's not worth it.
