As far as we know, gravity acts the same way for black holes as it does for everything else. There is no reason to believe that it could be different for supermassive black holes.
And this is the part that requires a bit of trust. People have tried alternate theories of gravity, but they always kind of single out one case and manage to do an ok job, but no one has come up with anything that explains such a large amount of observations as dark matter. Dark matter just works for a wide range of situations. This is why people are so confident in its existence. To prove this, you need to do some math, unfortunately. I can't explain the ideas to you, but ultimately what distinguishes between something that's just a neat idea and what is actually real is the cold hard math. We might dislike the idea of dark matter, but bear in mind that people really disliked quantum mechanics when it was first introduced. Our dislike for something doesn't affect how real it is. It's the experiment that makes the call.
There are many papers on the subject if you want to investigate, but it makes for quite dense reading.
It's not a big leap actually. Dark matter might even be neutrinos, although I'm not entirely up to date on that area of research. We just need a particle that interacts gravitationally and perhaps weakly with baryonic matter (that's the part that most people miss, a weak interaction is allowed). We already know stuff that does that. We just aren't sure there's enough of it, so we're searching for other particles that might fit the bill. Dark matter really doesn't have to be that exotic.
And I assure you that the observational evidence for dark matter is anything but subtle. Galaxy rotation curves are a quite spectacular way to show this effect at work, as I explained above. We also have the famous bullet cluster, a merger between clusters of galaxies where gravitational lensing shows a large amount of mass is found in the non-luminous parts. Another dramatic demonstration. Anyone telling you that the effects which justify the existence of dark matter are "subtle" is not being very thruthful. I mean, there's nothing subtle about galaxies smashing into each other...
So in short, dark matter doesn't have to be all that exotic and the evidence for it is quite easy to observe. So what's the big deal? Why do peole dislike it so much? people bring up the ether example, but they tend to forget about all the other particles we predicted and then later discovered...
First, thank you for phrasing your comment in a respectful way. It goes a long way to getting some good answers. I actually want to help you.
It is probably not supermassive black holes that are responsible for dark matter. That is in fact why I encouraged others to google for "galaxy rotation curves". Your orbital speed around the center of the galaxy is affected by the amount of mass inside that orbit and your distance from the point you're orbiting. Since most of the mass in the galaxy is close to the center, we should expect that a plot orbital speed vs distance would result in the orbital speed decreasing after a certain point, since there is little mass being added inside the orbit with distance. However, that is not the case. What we observe is that the orbital speed just keeps going up and up as you go further out. This relation is not just true for our galaxy. We have catalogues full of rotation curves for galaxies that obey this relation. This seems to indicate there is extra, non-luminous mass out there, further out from the center.
This means the supermassive black hole cannot be responsible for this, as its mass is located entirely in the center. The extra mass must be futher out for this to work. We quickly thought it might be objects like brown dwarfs (failed stars, essentially) that caused this, but our experiments overwhelmingly demonstrate this is not the case. That is why the commonly accepted theory is that dark matter must be particles.
Let me add that galaxy rotation curves are but one piece of a large body of evidence in favour of dark matter. The existence of dark matter is hardly a matter of debate amongst astronomers and astrophysicists. Sure, you've got some theory people trying to come up with alternate explanations cause that's their job, but by and large dark matter must exist for things to make sense. We have seen the shadow of the beast, we know it is there. Now we just have to find it.
The only loudmouths are the people who are claiming to know better than scientists despite being completely ignorant of the facts. As I explained above, there's a difference between "I don't understand, can you explain?" and "I don't understand, this is stupid." The first will get you a helpful reply. The second will get you scorn, a keyword and an invitation to goole.
Also, I don't think you spent very long thinking about the bullet cluster. It is solid evidence for dark matter. Alternative explanations cannot explain this behaviour to the same precision, something that even a cursory search reveals. You can't just look for one discerning opinion and use that to justify your position, that's cherry picking data. The preponderance of evidence is in the direction of the existence of dark matter. I gave you a place to start, now go and educate yourself. This is slashdot, people here are supposed to be good at learning on their own.
The distinction here is the complete lack of humility showcased by people like you. You know that you know very little about the subject, and yet you start to make claims about how things work as if you had any authority. When you don't know much about something, you approach it with humility and try to better your reasoning before passing judgement. For example, I gave you some excellent starting points for your journey. How much time did you spend writing that post? Now, did you actually google "galaxy rotation curve" and "bullet cluster"? Cause if you didn't, I think it just shows everyone how you have zero desire to learn and only want to be argumentative for the sake of it. You lack humility. If you had approached me and asked me kindly to explain to you why dark matter must exist, I would have gladly explained this to you. But if you act like a jackass and pass judgment on something in complete ignorance of the facts, you're going to get a keyword and an invitation to google it. Dipshit.
If you can't see the difference between "Hey, I don't understand why this must be true. It makes no sense to me. Can you explain?" and "Haha! Scientists are such morons for thinking this!", you've got serious issues, and it's not my job to fix them.