White people are no different from us. Those that do little more than wash and condition have no little trouble growing their hair. Then there are those who color (sometimes bleach), get perms, blow dry and their hair get damaged, and breaks and they can't retain length.
I had one friend who wanted blonde hair and she didn't want straight. She bleached her hair and got a perm. She couldn't understand why her hair was only shoulder length and she couldn't get it to grow longer. I told her, you can have long, straight, limp, blonde hair -Or- you can have long, brown hair with curl - but- you can't have long, blonde hair with curl. In other words, she COULD NOT bleach and perm her hair and still expect it to grow to the longer lengths.
As for genetics playing a part in the length of hair. This only applies to the extremely long lengths. Genetics plays a part in the life cycle (how long the hair remains on your head until it sheds) Average life cycle it 2 to 3 years and with the average growth being 6" a year, then the average person should be able to have hair from 24" to 36", if they can retain the hair.