Here, for instance.
I call myself an Aspie partially because that's my diagnosis, but also because the spectrum is so vast, and my own place on it so unremarkable, that it feels presumptuous to describe myself as "Autistic". It feels disrespectful - like I'm claiming insight into and ownership of a whole suite of experiences I just don't have.
I used to describe myself as autistic for a while, but over time it just stopped feeling right. So I stopped, and went back to Aspie. It feels more honest.
Just to make it more complicated, at the moment I'm Schrödinger's Aspie: either on the spectrum or not depending on which doc you talk to. While there is a very valid place for self-diagnosis, I wonder about people like me, who can pass well enough to have the professionals arguing about whether we're even on the spectrum or not, claiming the Autistic mantle as our own. I worry that by describing my relatively minor difficulties as "autistic", I'm making light of the much greater challenges faced by other people on the spectrum. It feels more like appropriation than solidarity.
This is why I like umbrella terms like "on the spectrum" or even more broadly "neurodiverse". They cover Aspergers, autism, and other related conditions without leaving anyone out. They cover the multitude of different identities within the spectrum - even within Aspergers itself you have everything from 'Asp' to 'Spergy' via 'person with Aspergers'. In that situation, an umbrella term that covers everybody without singling out any one term as best or correct seems fair.
It's also about picking your battles. Right now we have a lot of reasons to fight, from the loss of the Disability Discrimination Commissioner in the recent budget to the more general shafting of young disabled people, to the fact that the suicide attempt rate for Aussies on the spectrum is 433% that of the general population. (No, that's not a typo. Four hundred and thirty-three per cent.) Those are things we need to fix.
And I don't think it really matters what you call yourself while we do.