I've often felt the same way about the need to label one's self in order to have an identity. But I can empathize with people who have some kind of undefined handicap/limitation and ultimately find solace in a label and sense of community.
For example, pretty much anyone over the age of 40 who has dyslexia will tell you how cathartic it was to be diagnosed when previously they were just regarded as stupid or lazy. A diagnosis meant that they had a medical condition that they could overcome (or at least manage). If they were simply stupid then it meant there was no hope for them. So their new, better, label mattered.
However, one could argue that pretty much anyone who suffers from any kind of limitation...is suffering from some kind of medical malady. Perhaps, in the future, people we will create new labels and therapies for many of the currently unlabelled, but afflicted, people as well.