It's basically magic aka not actually real, just something in vogue to pretend is real at the present moment.
Why do you say that like it's obviously ridicule or impossible? Neutrinos do exist and they fit all these criteria. We just know they're not dark matter (or at least not all of it) because they're not heavy enough (and some other things).
Don't try to rely on intuition when thinking about particles, there's no reason for evolution to make what happens at quantum scale or relativistic scale intuitive to us.
The neutrino is a good example of a particle that almost doesn't exist. They are produced in solar reactions in spectacular amounts. Trillions of them are flitting through you right now as if you don't exist. You'd need a light year block of lead to ensure you could stop one. Mind-boggling amounts of them have to pass through our detectors to see even a single interaction.
Simply put, the particle physics does not have to behave nice so you can sleep well at night.
We can measure the mass distribution on astronomical scales. We "see" the dark matter. Just not with light.
It's not crazy different from saying the same about that poltergeist.
We know of particles which behave the same way. Neutrinos for example.
We are not measuring dark matter, we are measuring something that is not what we expect and we decided it's dark matter.
You act like we've managed to probe the depths of physics with certainty when in reality you find any means to reject that which offends your sensibilities.
At the root of science is "sensibilities", like occam's razor, even "what counts as experimental reproduction", etc.
Not that I am saying it does not exist. Only that we do not have the means of falsifying it if it is false.
It's a scientific theory. It's the best that we have right now to model the real world and be able to do prediction on its behavior.
Does it seems to be kept together by duct tape? Maybe.
Is it yet useful? Yep.
Will it be discarded if anything more fitting will came up? You can be sure of it.
And it's not like the concept of aether itself was really all that useful for anything. The physicists wanted the light to have some mechanical medium to propagate through instead of being a thing of itself, that actual itself shaped mechanical media, not the other way around (mechanical properties arise from the E-M interaction, not the other way around), simply because all other known waves phenomena existed in mechanical media.
Dark matter, string theory, aether, etc., those are models that we, at some point in time, think may help us get better predictions and design further experiments. All models turn out to be wrong in the end, but they can be helpful until we come up with better ones.
If you drop the dark matter model, then you would want to have some other model as for why we observe what we observe. Some people find that other available models are even worse than the dark matter one, but if you don’t think so you can take your pick.