Autism and schizophrenic spectrum conditions are often considered opposites. However, people who are both autistic and on the schizophrenic spectrum exist (for example, SteelMaiden on wronplanet.net). The reasons given for those two types of neurologies being opposites is based on stereotypes of autistic people.
One stereotype given as a reason is that they are opposites is that autistics are better at math than art. However, some autistic people are bad at math, and some autistic people are good artists (and I'm not just talking about drawing real things accurately).
Another stereotype that is used to support the argument is that autistics lack a theory of mind. However, the very concept of theory of mind is fundamentally flawed. When autistics don't understand neurotypicals, it is attributed in the theory of mind deficits of the autistic person. When neurotypicals don't understand autistic people, this is also attributed to the autistic's poor theory of mind. Is it possible that neither of them can understand the other's experiences? Furthermore, there is evidence that failing theory of mind tests may be due to difficulty processing sentence structures in Theory of Mind tests.
Finally, people use the stereotype that autistic people lack imagination. It boggles my mind why people think that, as I've never seen that in autistics, and I don't think I can give a good explanation, so I'll just leave you with this link: