we're pretty sure our theories are right

People are always so sure.

They didn't say "Well, the geocentric model is probably wrong but we'll use it for now" either.

But so far we don't have experiments proving it's wrong, I think that's the crux of the argument ?

I'm certainly not a physicist.

I stopped my physics at a BS. But if I understand correctly, we do have observations that don't match our theory. They would match if there was matter that we can't see. "Dark matter" is the hypothesized missing matter. This lets us keep our theories as they are.

But instead, you could regard the observations as "experiments proving our theories wrong".

There has been work done toward re-working our current laws to fit observation without dark matter, but I think it just breaks way more stuff than it solves. The new model ends up being a worse fit for pretty much everything else but the galaxy rotation thing.

We already have weakly interacting particles like the neutrino, which don't interact with matter outside of the weak force, making them rather difficult to detect, it's not really that far out of the realm of possibility to have other particles that only interact via the gravitational force.

> "I think it just breaks way more stuff than it solves. The new model ends up being a worse fit for pretty much everything else but the galaxy rotation thing."

This is often mentioned as a reason not to spend time with alternative models. However, breaking stuff is sometimes necessary if we are to get out of the local maximum of theory usefulness. The Kopernik model was much worse fit for the observations of planet motion that the Ptolemy's model, but it did have other virtues, like simplicity. The broken parts got fixed later with development of mechanics and perturbation theory.

That is a given. Dark matter isn't really that clean either, it breaks what we know about the standard model and known particles, something that the folks at CERN keep confirming as they break in to new and uncharted areas of what we can observe experiment. Your statement is less enlightening as it is simply stating the inaccurate nature of a model.