Dark matter might not even exist, all we know is that gravity-based predictions break down after a certain point. Dark matter is the just the most popular proposed solution where you essentially just add extra undetectable mass until it works. The distant second is Modified Newtonian Dynamics (MOND) or some variation of it, which is where you try to tweak the theories to fit observations instead. It has the same problem as dark matter where we keep coming up with better experiments which always fail to find anything.
There’s a similar problem at the opposite end of the scale spectrum too; quantum mechanics doesn’t play nice with our current understanding of gravity leading to the search for the “theory of everything”. This is why I personally lean towards the idea that it’s our theories that are wrong and not an undetectable mass, but this isn’t my field so my opinion isn’t worth much (especially since a majority actually working in the field lean towards dark matter as far as I can tell).
Trans men and castrated men exist, I don’t think it’s the balls.