"I have a cat."
"They wouldn't get along with my dogs."
Not a completely logical response, as something like "I have dogs," if actually voiced, would have tied things together nicely, but not so odd that it disrupted the flow of conversation or caused any real confusion.
Of course I must caution our readers against running around diagnosing people with any type of disorder! I doubt they would appreciate it, and you run the risk of having it turned around on you and being labelled as an insufferable know-it-all or someone who is incapable having a simple conversation without analyzing it to death. Also as people may fail to express thoughts or parts of thoughts while excited, tired, anxious, distracted, etc., a few omissions cannot be taken as reliable proof that any sort of communication-related disorder is present.
Omission (əʊˈmɪʃən) has a very straight-forward etymology, being derived from the Latin omissiōn-em (the act of omitting something or something that is omitted), from the verb omittĕre (to omit).