Dr. Awkward said:Godzilla is not a mammal. Big Bird is not a mammal. They have "not being a mammal" in common, and so for the purposes of argument from analogy, Big Bird is identical to Godzilla.
An analogy doesn't presume that two things are identical, so I don't know what you're reasoning is trying to show here.
Dr. Awkward said:Or perhaps analogy is more than just linking together two unrelated concepts by virtue of trivial similarities.
Trivial is in the eye of the beholder. It's uninformative to just throw in adjectives in places where the issue is actually in dispute. I would guess that whatever similarities a person is trying to show with an analogy, that person finds those similarities to be significant.
Now you have an opinion about how important you feel that information is, that's cool. But acting like there some logical grounds for making a distinction between trivial and non-trivial IMO is unwarranted.