Could it be large transparent gas clouds? No, it turns out that gas clouds aren't completely transparent, and can be measured in various ways. We looked, we checked, such clouds don't contribute enough mass.
Could it be dust clouds? Dust clouds are not luminous but they do block visible light, so they'd be obvious. We looked, we checked. It wasn't dust clouds.
Could it be rogue planets or brown dwarfs? No, such objects would cause gravitational micro-lensing effects, which can be observed in dedicated campaigns. We looked, we checked. It wasn't planets or brown dwarfs.
The only theory that has withstood the last several decades of experimental observation and simulation has been the dark matter theory (weakly interacting massive particles at sub-relativistic speeds). It's the only thing that explains all the evidence across the board.