While I agree with you in principle, you don't need a medical degree to diagnose a broken leg if the bone is sticking out.
When it comes to developmental disorders (and also, for similar reasons, mental illness), I'm not sure that analogy holds.
Mental disorders are tend to be more of a spectrum than a binary affair (unlike a bone, which is generally broken or not), and even mental health professionals may have difficulty in diagnosing them (i.e. antisocial personality disorder, which actively attempts to avoid diagnosis)...
Exactly, and they're not quite as simple as "oh i haz seen this buncha symtoms and i have sum!". Sure anyone can diagnose a broken bone, not everyone knows wether it's just broken or if blood is streaming inside causing necrosis, anyone can diagnose that you're shy / a little associal etc, not everyone can put all of them together, interrogate you on your past to separate between physical and past experience as the cause, and make a correct diagnosis on psychiatric issues.
For all of those who are in the "i've been told i have asperger", i'd be surprised if even a single one of you has it among those who weren't told straight from a doctor or at least medical staff, it's not a cold, it's not something you see on every corner of the street, your anxiety fears asociality and other things that may lead you to self diagnose as who knows what are most likely the cause of a much more common sickness in the general population, it's called being human and is perfectly normal unless it's strongly impairing your life (blocking you from work / social life / causing suicidal thoughts etc), in the former case, get over it, in the later case, seek help as in most case you can get major help from a psychiatrist and get back to a normal life. For those who are genuinely autistic i perfectly understand this is very different, but those are usually found our early, by their parents and through the medical path, not as soon as they hit a roadblock in adulthood and get told by a forum or a friend.