To answer the original question...
We fight for different reasons. I would guess most here are sure of the validity of what they believe, and feel compelled to convince those they see as hopelessly wrong.
Myself, it is the particular twisted logic of the flat Earthers that draws me, as the moth to the flame. I know it is pointless, I understand that, yet I feel compelled to try to fight it anyway. I generally try to hold myself to a high degree of reason (Note please the try!), so when I find it being misused I feel drawn.
Oh, and as has been pointed out, it is perfectly possible to prove whether the Earth is round or flat. There are mathmatical methods, astronomical methods, even methods of reason. Of course, if you want to take the easy way you could just build a rocket and head to space.
However, since most don't have the space method open to them, they have to rely upon the others. Most of the flat Earthers, trusting nothing they either can't reproduce themselves or don't fully understand (or failing that, anything that is too disagreeable), hold to their theory.