It's generally difficult when trying to describe anything for which there is no real reference, using language that by it's very nature is referential.
Yes.
The big "Bang" invokes the idea of an explosion, for example, so from the getgo it's more difficult than it might be.
As somebody else already mentioned, the term "big bang theory" was originally invented by somebody who didn't think much of the theory. It was meant to be disparaging, because it suggests a simple and probably wrong mechanism, but the term was later adopted by champions of the theory as well.
I see such language in such instances as just metaphor, and the key being to not get too attached to the metaphor but to what is actually happening.
That's a common trap that people sometimes fall into when encounting scientific jargon for the first time.
And when science isn't entirely clear what is actually going on, choice of language may push/pull you in one direction at the exclusion of other valid interpretations.
Yes.
For example, many might think that the expansion of the universe is because space itself is expanding, and this results in objects being further apart. But it is equally valid to describe it as space not expanding and objects moving apart "while under the influence of their mutual gravity" (or so suggests wiki).
I don't see much of a distinction there. There's a bit of a problem with the second description, because intuition suggests that gravity always tends to cause attraction between two objects, which tends to decrease their separation, not increase it. Yet the expansion of the universe has all these things with mass moving further apart all the time.
Also, per wiki (and who are we to disagree...):
wikipedia is not perfect or error-free.
"
The expansion of the universe is the increase in distance between gravitationally unbound parts of the observable universe with time."
- https://en.m.wikipedia.org/wiki/Expansion_of_the_universe
That's a reasonable definition, though it does risk communicating the incorrect idea that gravity has a limited range of influence. It's sort of true, in a way, but not
quite true.
So is this due to the metaphorical push or pull?
In physics, there is no important distinction between "push" and "pull". Both are forces. "Push" and "pull" are only useful, in some circumstances, to indicate the direction that a force is acting. Attraction between two objects is sometimes described as a mutual "pull", while repulsion is sometimes described as a "push", but this is not universal and the usage is usually context dependent.