It has been observed, by its effect on other things, and in particular because this effect isn’t always the same. Most galaxies’ stars orbit at the wrong speed, but some behave as expected. Most galaxies gravitationally lens the background more than expected, but in some cases (colliding groups) something that doesn’t shine or reflect any EM radiation is causing lensing next to the galaxy while the galaxy itself is closer to what we expect without dark matter.

That's right, observations were made that do not fit with our current understanding of physics (equations). That means our understanding is wrong. So instead of assuming the equations are wrong physicists invented an invisible type of matter. That is not science. Dark matter is nothing more than modern day aether.

If you wanted to get particularly philosophical, everything is observed by its effect on other things.

Sure, but my point was that dark matter is not just an artefact of equations.

How about black holes?

Black holes are made of regular matter not dark matter because they interact with electromagnetic waves.

Dark matter interacts with light in the same way as a black hole does. They both have mass and therefore both bend space (and light passing through that space) around them.

It's already known that what we call dark matter in some contexts (e.g. the mass that holds galaxies together) is at least partly made of black holes. We just don't know if black holes account for 100% or 1% of the dark matter that we believe exists in a typical galaxy.

They’ve been both predicted and observed. Dark matter is a conjectural solution for an anomaly in the rotational speed of galaxies across their discs. In my opinion, it’s almost certainly a bodge, and if the W boson has a different mass to that expected it could account for what we call dark matter, as the implications go far beyond just the additional mass - if the mass is off, then perhaps the nature of the weak force is misunderstood - for instance, perhaps the mass variance is driven by a hidden variable, and that in turn could account for what we regard as “dark” phenomena.