> Is this an inherent trait or one that can be learned?

I'm sure there's some element of in-born talent involved, as with almost anything, but nobody's purely a natural at it. It's kinda like people who can tell you all kinds of stuff about some Beethoven piece that you, a non-classical-music fan with little or no knowledge of musical history or theory, didn't notice—they don't come out of the womb being able to do that, they trained and they spent a lot of time not just listening to music, but thoughtfully listening to music, to get to the point that they seem to be able to do such analysis effortlessly, and even on a first listen. Maybe they had some natural talent, too, but it's largely a trained skill.

> I wouldn't even know how to begin to learn to do this.

Read, watch, and listen to criticism. Maybe try Every Frame a Painting on Youtube (sadly not making any more videos, but the existing ones are excellent). It covers, especially, visual storytelling. They're nice and short and fairly content-dense. Pick some for movies or directors you're familiar with, first, I'd suggest.

If you can handle the affected narrator-character, some little meta-narrative horror-tinged digressions, and a longer-form work, try Red Letter Media's reviews of the Star Wars prequel trilogy. It's basically hours and hours of someone asking the sorts of questions one asks to understand a narrative (and mostly coming up with unsatisfactory answers, because the scripts of those movies are bad). This especially covers story structure, suspension of disbelief, and character motivation.

There are tons of other Youtubers doing this kind of thing, many of them good at it, and others here have already suggested some of them.

Basically, seek out and read or watch analyses of films by people who already at least kinda know what they're talking about. It'll help you get a sense of how to approach media, and to tell when you're headed down a productive path versus when you're looking for something where there's not much to find. Then, watch movies and try to apply what you've learned.

The main habit to get into is asking questions. Why is this character included? Why is this scene included? Why is this scene so red? Why is the camera tilted in this shot? Why is the camera moving in this shot? What does this sequences of shots make me feel and how does it achieve that effect? Is there an overall mood to this piece (or scene) and what is it? How does it convey that? Are there elements in common across this film? Do those constitute or contribute to some kind of message or theme(s), and if so, what are they?

Past that, you might start to become aware of things like rising and falling tension at various levels—a scene, an act, the entire work. Those often play into the answers to the why questions.

Beware, when you get good at this and it becomes second-nature so it's not even something you can really turn off, a lot of minor reveals (that guy was a bad guy all along!) become so obvious that you figure them out tens of minutes before most viewers—sometimes within seconds of the introduction of the element you figure out :-)

Also, you may find bad or lazily-made movies worse than you did before, largely because they tend not to have much to say, and have lots of missed opportunities for better use of their medium, which can be grating when you learn to spot those—but you might, oddly enough, find very bad movies to be better! Marveling at how much they get wrong, and how very wrong they get it, can become its own kind of fun.

Much of this (except the stuff that's very tied, specifically, to cinematography) carries over to other media, like books and even (to some extent) video games, so you can practice a lot of the same skills there.