Here is the sentence:
Josh thinks Annie is the most beautiful woman in Springfield, so he has
no interest in dating either
Solita or
going out with Reva.
When you use either ... or, you must have two equal grammatical items. After either, notice that you have a noun, Solita. But after or, you have a gerund phrase, going out with Reva. The structure is not parallel. Nice choice, grammar gourmet!
To fix the sentence, you can change going out with Reva to Reva so that you have two nouns.