Do we?
I thought it was that we know a significant amount of mass is missing from our observations and we explain it with dark matter.
Dark matter to me is a crutch to explain things until we really know.
Is it not at all possible our understanding is just wrong and that nothing is missing?
We know that every particle we've been able to track down and verify the existence of responds to the gravitational force. We also know that some particles (like neutrinos) have virtually no interaction with anything other than gravitational force, to the point where the vast majority of them will pass through the entire earth undetected and having virtually no effect on anything or anyone.
The notion of particles that are even harder to detect than neutrinos doesn't seem that absurd. It's kind of anthropocentric to assume that most of the mass in the universe is going to be the same kind of mass that we are, or that we are at least capable of easily observing.
And think about what it would imply if there were no dark matter. It would almost imply that, as of the late 20th century, humanity finally had a basic comprehension of all of material existence.
The universe that humanity understood before Copernicus and Galileo is less than 1% of what we can see now. If our math is right and there really is enough dark matter and dark energy to throw off our models, then the universe we can see now is about 5% of everything that exists. That seems pretty plausible for a civilization that can barely get out of its own atmosphere.
The longer answer is that dark matter isn't particularly special or unique in this. We make observations, and where they don't match our expectations, we hypothesize new things to fill the gaps. Sometimes they're borne out by later observations, sometimes not.
We've hypothesized the existence of planets to explain deviations in planets' orbits. Sometimes the hypothesized planets existed, sometimes they didn't. In the early days of chemistry, we came up with a whole bunch of elements; sometimes they turned out to be compounds that were particularly difficult to break down. We came up a whole host of particles and subparticles, and the ones that we still think are real aren't necessarily the ones you would have guessed at the time they were proposed. If you pick up an old text book on quantum mechanics, you'll find they keep referring to it as "the new quantum mechanics", not just because it was being nailed down at the same time the text books were written but to distinguish it from "the old quantum mechanics" from twenty years earlier that it was replacing.
Sometimes the hacky models are the best we have to offer; most people will call the Standard Model of particle physics just a hacky description of the observed phenomenon, but all the elegant models to replace it haven't really paid off.
It's possible that dark matter will go the way of luminiferous aether, but so far all the observations astrophysicists are making really jive well with the idea of dark matter, so for now it gets to stay in the "weird things about the universe many people don't like" category instead of the "stupid ideas no one can believe that people used to believe" category. I mean, it makes me angry that a neutron isn't just an electron and proton mashed together, but them's the breaks.