You can certainly try to copyright it, but if the person who slavishly copies the case can demonstrate that you didn't write it yourself, you lose the copyright protection because you're not the author. There are copyright cases which turn heavily on who the actual author of the work in question is--the Happy Birthday song being perhaps the most famous.
This whole thread could be true wrt the Monkey Selfies, but I am someone else's paid monkey and they can definitely copyright the work I do at work.
So does this case really boil down to the Monkey being free and not owned in that you can't take their copyright away, but you could if you owned the monkey?
I feel like the structure of our civilization is not stable, the focus and balance of capital power, the law and the ecological direction we are headed. I saw this play once and I didn't understand a bit of it.
> This whole thread could be true wrt the Monkey Selfies, but I am someone else's paid monkey and they can definitely copyright the work I do at work.
That is "work for hire." You are the creative author of the code, but since your creativity is being applied at the direction of another, it is that person who owns the copyright instead of you. The Copyright Office has a document to explain how to decide whether or not your work is a "work for hire."
As applied to monkey selfies, it's possible that the human photographer who set the situation up owns the copyright instead, but this wasn't argued in court.