From what I've seen, here are some of the arguments against self-diagnosing:

• Allistic people using autism as an excuse for their behaviors/difficulties, then denying the difficulties that actually autistic people experience and misrepresenting autistic people.
• Narcissistic and psychopathic people pretending to be autistic to manipulate others, including actually autistic people.
• Misdiagnosing themselves when their difficulties are actually related to other root causes, such as prolonged childhood abuse.

In the first two arguments, the problem with self-diagnosing is the social impact it has on others, including the autistic community. I can see why some people are against self-diagnosing since it could make their lives harder, especially autistic people. The last one is more about helping the individual properly understand them-self and developing a proper course of action to improve their lives, so it's an argument rooted in care.

I am not entirely against self-diagnosis. However, I think it could be re-phrased to "self-identified" since "diagnosis" is a medical term. It would be like a person saying, "I'm self-diagnosed with depression." That person isn't diagnosed with depression, though they very well may be depressed. It's really just a pedantic issue from my perspective. Regardless, I don't really care one way or the other because I understand what they are saying and think that an actually autistic person self-identifying as autistic is valid enough. Still, while I wont invalidate someone for self-identifying by gatekeeping autism, I tend to be a little cautious at first because of my experiences with people pretending to be autistic. In this case, I think the issue is that some jerks just can't let us have nice things.