I'm mostly not in favor of software or media piracy (though if it has been sufficiently long (not sure how long) since it has been commercially available, or a handful of other cases that don't come to mind right now, I think probably fine), but I do think it makes sense to distinguish it from theft, and indeed, distinguish it on the basis that you are not depriving the person of a thing which they have.
If Joe is selling cherries he grew on his cherry tree, and I start selling some cherries from my cherry tree for cheaper (or just giving away cherries), this does deprive Joe from some of the profit he would get from selling his cherries, because some people who would have bought some cherries from Joe instead of from me, but I am by no means stealing profits from Joe. I'm not taking his cherries. He still has his cherries. That's not to say that he isn't worse off. He is, of course, worse off. But (except if some other conditions hold) I haven't wronged him, and I certainly haven't stolen from him.
(Ftr, I don't actually have a cherry tree, and do not grow any food.)
Now, if Joe is selling copies of a file, and I am giving away copies of the same file, well, it seems like a similar situation. One difference is that in the case of the cherry tree, both Joe and I are putting in the work to create the product, namely, by raising and maintaining our respective cherry trees, and harvesting the cherries,
while in the case of the computer file, it may be that Joe put in a lot of work into creating that file in the first place, and I did not, and so if I were to sell copies of the file, that would seem quite questionable.
Now, if I were to distribute the file Joe made and is selling, the reason this would be bad is probably a combination of "This makes Joe worse off, and he should be rewarded for the benefit he provided others, and also society decided on that basis that I shouldn't do that, and unless there is an overriding moral obligation to do otherwise, I morally ought to follow the ethical rules that society has established."
This is, I'll admit, somewhat similar to at least some of the reason it would be bad for me to steal some of Joe's cherries and give them away (though with less of the reason being "because of the ethics society decided" part than in the case with distributing the file.)
Though, one difference in this case is, Joe could do other things with the cherries other than sell them, and by stealing them, I am depriving him also of that option. This doesn't happen in the case of distributing the file. Nor would it happen if I had a magical duplication beam which I used to make duplicates of his cherries.
I think this difference is an important part of the concept of theft.
The concept of theft, I expect, arose substantially before money, and I imagine also before significant trade.
The concept of "Hey, that's mine! I need that!" is fairly basic, and is based on "If another person takes it from you, you don't have it anymore." .
Now, of course, socially we could agree to use the word "theft" to also include software/media piracy, but I personally don't think we should. I think it is best to use different words for them, because I think it makes sense to keep the concepts separate (though related).