Ambiguous meaning - two nouns in a row

I'm often confused by the meaning of two nouns in a row.

Specifically, I came across this word in a TV show:

Demon Hunter

Without looking at the context of the show, I feel like this word can mean either "A hunter who hunts demon" OR "A demon who is also a hunter". Which one is the right one?

Similarly, words like:

Child abuser

Most people would understand it as "a person who abuses a child", but why can't it mean "an abuser who happens to be just a child"?

The short answer is that there's no reason they can't mean "a demon who hunts" or "a child who abuses".

The long answer is that we won't instinctively parse them that way: in general English usage a construct like this is understood to be [attributive noun] [noun] where the attributive is modifying the one that follows.

In the case of your first example, we know we have a hunter. What kind of hunter? Demon. A hunter who hunts demons. In the second, we know we have an abuser. What kind of abuser? Child. An abuser who abuses children.

It can mean both and there's nothing stopping you, but some nuance is involved. John Clifford already posted a great answer, but I thought I'd provide some additional points.

Demon hunter has context and history behind it. English speakers have a sort of contextual understanding from literature and history that helps to convey the meaning, "A hunter who hunts demons." You would reach similar results with terms like witch hunter.

The reason female hunter doesn't have the same result is because we don't have roots in literature and history where "a hunter who hunts females" has any sort of strong presence.

Usually when an English speaker is trying to describe something (the hunter) but that description happens to clash with a well established context, then to convey that to the reader in a better way, they might rewrite the sentence as something like

"The hunter of females"

Sometimes it can be a little awkward like "The hunter who was female" but how it's conveyed in the best way is entirely up to the speaker/writer. It depends on the situation and context.

With demon hunter, you could say "The demonic hunter." This also works with cat burglar. To me, if you wanted to describe a burglar who was actually a cat, you could say, "The feline burglar."