> You cannot falsify dark matter, and you cannot prove a negative. Imagine I say there is a 5 headed green deer that weighs 2000 pounds and can speak Gaelic, but it's really good at avoiding being spotted - so good in fact that you can even look at right at it and might not see it. And you can even touch it and not even know you're touching it! What would you could consider an exhaustive proof of its lack of existence?
Dark matter isn't like this, though. It's more like an invisible deer that's been eating your grass and shitting on your lawn. At some point you have to say "I might not be able to see it, but the only thing that eats grass and leaves deer shit is ... a deer."
We have the problem that the observable mass of a galaxy is not sufficient to explain the motion of its constituents. As gravity is a pretty well validated theory, it can all be solved if we postulate some matter that we can't see which is still gravitationally affecting those things we can see. Dark matter, in this respect, is no more than the simplest explanation of what's happening via a single item that, if it were true, would explain things.
If you think you have a deer you haven't seen so far eating your lawn, you can put out infrared cameras and all sorts of equipment - and just maybe you might find that someone down the road has been messing with you and is mowing it at midnight. But equally, you might see grass disappear and see shit appear from mid air, and come to the conclusion whatever's doing it is invisible.
Ultimately, it's very conceivable that someone might disprove dark matter. All they have to do is posit some other candidate (eg a modification to gravity), and then predict a result that would follow from that. So far, all the other candidates haven't resulted in a hit, but the field is open for the next great idea to come up with one.