Merl Haggard sang a song about not going around mirrors... it's not really fair to tell someone to suck it up when it comes to things like hair. It's really easy for a kid to think that grown men are being babies when it comes to stuff like this, but think about how we all self-identify with how we look. What if we lost our nose or our lips, and when we look in the mirror we see someone completely different. I shaved my head one summer in college because of the heat, but I had problems even looking in the mirror then. And, when I shaved my beard last year, I had issues with looking in the mirror then.
We see ego as being this evil thing, but we all have a self image. Remove something from our face or head and it is really hard to look in the mirror. Luckily for me, I can't see my bald spot without two mirrors, ha ha. But, I can totally empathize with someone who can see the bare skin on their head.
Youngsters see things like boob jobs, facelifts, combovers, toupee's, etc as totally egotistical vanity issues, but really they can mean so much for people who have a problem with how they look. This is why cancer survivors go through get so much therapy and get special attention when they lose breasts or hair, It can crush a person. The very same "woke" individuals who would stand up for so many disenfranchised people in our civilization will also put a man down for a toupee or a woman who loses a breast getting implants, it's ridiculous.
On the other hand, in accordance with the OP, I just don't know how to help you help your friend. It is a very individualistic thing in how we react and what is best. Too many variables to get help from complete strangers on a forum, but I wish you and your friend the best of luck and good wishes.