Which itself is derived from the logic-defying diagram of the holy trinity: https://en.wikipedia.org/wiki/Trinity

How is it logic defying? It seems straightforward to apply on any compositional entity: I could make one with "Apple Executive", "Tim", "Phill", and "Eddy"

I guess because of the assertion that "there is only one God".

While that breaks the Apple executive example, it's still just as easy to explain from a programming perspective: each of the sides could be a trait/interface which is implemented/part of the same entity/Singleton

Yes, but real world entities don't stop being a thing just because you refer to their one specific trait. The god example only works if you assume it works. That's why it's not logical.

Anyway, traits are "is a" descriptive thing, not a referential equality "is". The trinity relations are not "is a" to begin with, or we'd be having many gods and Christian priests are not into that.

Given it is a discussion of an entity that is already defined by properties not shared by any other real world entity its seems not just logical, but reasonably, to assume that it differs from them in other ways too.

I tend to agree traits is not an accurate description, but it is a reasonable analogy.

> The trinity relations are not "is a" to begin with, or we'd be having many gods and Christian priests are not into that.

Sayings "priests" seems and off choice of wording. Why not just Christians, or even "Christian theologians"?

Just because someone comes up with one illogical idea, it isn't reasonable to say it likely "differs in other ways too". Instead maybe establish one unusual thing to be verifiably true before stacking on more.

> Sayings "priests" seems and off choice of wording.

Meh. Priests set the norm for the regional communities.

Maybe because the ”is not” clauses?

Tim is not Phil...

Tim is Eddy and Eddy is Phil, but Tim is not Phil?

Well, I suppose it depends on what your definition of "is" is. Mine typically exhibits the transitive property ;P