in my family, its my son with the long hair. I never threatened to cut it until about 12. he too freaked out about the idea. I realized I will never make him cut his hair, so I stopped threatening to. I also realized that he was not fully able to take on the responsibility of caring fully for his hair. I started giving him lessons on caring for his hair. first, how to wash it well. (soak your head to the skin, nickel sized puddle of shampoo, rub your hands together, make your hair bubbly all over. rinse until the water runs clear, do it all again exactly the same way.) then work conditioner into your hair and rinse. I brushed his hair for him. if it was not clean, or 'felt' bad, back into the shower.
then I realized he was using not enough shampoo and too much conditioner. we switched to pert because it contains conditioner so he only had to wash it twice and not worry about conditioner. this is easier for him. when he got better at washing it, I would brush his hair -mostly- out and let him finish. or let him start, then I would finish.
gradually do less and give him more to do alone.
now he is learning that brushing his hair need only take a few minutes. he will happily brush the bottom 3 inches of it for an hour!! so, say a half hour before time to leave or whatever, I'll say, you need to brush your hair before we/you go. it is a process to be sure, but he is learning.