Actually, I'm familiar with the cosmic distance ladder [1]. The thing is, you stack up some models on top of some other models. You can propagate the errors if your models are correct, but not if the models themselves are incorrect.
But this is a bit orthogonal. That was not the gist of my argument.
My argument was that lots of things in astrophysics are based on models. The rotation curves themselves, as a sibling comment mentions, are fairly directly observable, via redshift. But that's not fully true. Doing spectral observations is not entirely trivial, see for example [2]. Take a look at the sample profiles [3] and see how noisy they are. Of course, you can remove all sorts of noise with enough observations, and since (as I said before) the universe is static, and not going anywhere, you can point your telescope at the same galaxy and take lots and lots of pictures and do lots and lots of long slit spectroscopy from all sorts of angles, until you are left with very little noise (aside from the "thermal" noise due to the stars having some random velocity component).
How difficult, or easy is the math of eliminating that noise. Most likely it's not super difficult. Not trivial either. Probably somewhat similar to the math used for doing computerized tomography.
But here's the crucial difference. Between CT scans and astrophysics. And between my area of expertise that you encouraged me to consider and astrophysics. If the math for CT scans is wrong, people die. If the math I do for a living is wrong, people lose money (and I lose my job). This math with immediate consequences is self-correcting. If the math to denoise the galaxy rotation curves turns out to be wrong, someone just publishes a paper, and then gets to do a lot of talks at a lot of conferences.
Let's move on to the other evidence. For example the relative abundance of hydrogen, deuterium, helium, lithium. That is based on some models of nuclear interactions. Which agree with our experiments (in particular the crucial part is that neutrons have a half life of 600 seconds, and not, say 100 seconds). But nucleosynthesis happened only for the first 3 minutes after the big bang or so. Can we simply assume that general relativity effects were negligible? Let's put it differently: the whole universe was like a neutron star. Astrophysicists state that modeling neutral stars is difficult because quantum chromodynamics and general relativity happen at the same time, and we have nothing similar that we can study. But then how can we be so confident in our modeling of the early seconds of the universe, when, if anything, conditions were even more extreme.
The bullet cluster. I'm not going to point you to Sabine's blog post of how the bullet cluster is, if anything, a proof against dark matter. You can find it elsewhere in this thread.
Gravitational lensing. That's an impressive thing, but the claim that there can't be small black holes because we'd be able to detect them via gravitation lensing sounds to me quite silly. The space is just too large.
Now take our interstellar visitor Oumaouma. It just zipped by. Can the dark matter be just a large collection of such asteroids? Maybe not. But maybe at least a part of it can be explained by it.
Galaxy-wide lensing. The claim is that the effect of lensing is consitent with the mass of a galaxy being much higher than the one explained by its luminosity. But we know that all galaxies have a giant black hole in the middle. Can that black hole be bigger than we thought? No, you say, because of the rotation curve. But what if the rotation curve is erroneous?
Back to the rotation curve. Is there actually such a thing? Are the stars in the spirals moving at the same angular velocity as their cousins between the spirals? Most likely not. Is it possible that the galaxy rotation curve is a result of the non-homogeneity of the galaxy and the finite speed of the propagation of gravity (the speed of light) ? Here's how this would go: the attraction a start feels towards the center of the galaxy is governed not by what is between the star and the center now, but what it was a few thousand of years ago, when the spiral was a bit back, and so more mass was there. Conversely, the gravitational attraction away is governed by what it was there thousands of years back, when fewer starts were there.
You could say astrophysicists have thought of all these things, and about a thousand more. But do you see how everything depends on models? Models that can't be easily validated.
Is it plausible that there is dark matter? Absolutely. I don't see anything outrageous around the proposals that there are particles out there that interact only via gravity. But is it possible that there could be a different explanation that to various questions that does not require dark matter? That does not sound all that absurd to me.
[1] https://en.wikipedia.org/wiki/Cosmic_distance_ladder
[2] https://en.wikipedia.org/wiki/Long-slit_spectroscopy
[3] https://en.wikipedia.org/wiki/Long-slit_spectroscopy#/media/...
