Comment by Tainnor
There's a subset of people in the Japanese learning community that claim to have found the "one true way" of understanding Japanese and sometimes this amounts to making very grandiose claims about how to think like a Japanese person (in an almost Neo-Whorfian way). You can tell these people likely never had any sort of formal linguistic training.
Which is whatever - if you want to use some analogies that make sense to you, go for it - just don't pretend that this is what Japanese really is like.
(There is an element of truth to it, namely that Japanese works rather differently in most respects that European languages including English. But also, there are 6-7000 languages in the world and many things that happen in Japanese have analogues in other languages, even if the specifics play out somewhat differently.)
In the case of だ the much more mundane understanding is that it's the (nonpast, plain form) copula. Yes, there are some rules about when you can/should leave it off and when not, but those IMO belong to the realm of pragmatics not semantics.