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Black holes warp the fabric of space so much that not even light can escape once it passes the event horizon.
It has nothing to do with speed, it's simply that all possible paths lead into the black hole. Photons travel through the fabric of space like a car on a road. The car can't go off the road, so if the road curves, the car will have to curve with the road.
There's a lot more to it, but the most simple way to think about it is that a black hole's gravity is so strong, it warps space itself. And this warping of space basically acts like a funnel that funnels everything to the center of the black hole. Once an object or particle or whatever passes the event horizon (the point of no return) it is basically being funneled into the black hole by the fabric of space being twisted into the black hole.
Forgive me still have a knowledge boner...no sarcasm. But in your comparison then if a black hole is like a funnel then at the edge of it has a certain speed and speeds up when you keep going deeper? So in someway (hate to bring up fiction) Interstellar was correct or semi correct in it's portrayal of a black hole going into it? (not the timey wimey stuff). But with gravity being so strong if it warps space then that mean's just looking at one should give a viewpoint of something that is distorted to all around it? But the question I ask is the event horizon of a black hole...is that the way we can view speed through that lense, but with that said any event horizon at least should have an escape velocity like we have on earth? ......on a side not thank you for having a civilized discourse with me. It's hard to find. ...much love and if I don't reply have a great weekend.
Interstellar was somewhat correct about the event horizon. In theory there also could be an escape velocity but since nothing moves faster than light nothing can escape it. Since light (speed). is the ultimate barrier for velocity.
And every mass bends the space, the small the mass the small the dent.
In science fiction and with a real theorem people "move" faster than light. But using the Alcubierre drive would require so much energy that it is (for now(?)) impossible to achieve. The drive also doesn't propel the spacecraft faster than light but bends the space around it, so technically you would more so move the space around you, instead of traveling though space.
In regard to speed, the speed of light is actually the speed of causality, which is the absolute limit at which one event can influence another. It is an absolute speed limit. Light can travel at this speed limit because it is a massless particle/wave. Anything with mass would need to have infinite energy to travel at the speed of light because the faster something is traveling, the more energy it takes to accelerate it further.
Inside the event horizon, these same rules apply because it is still space and time inside the event horizon. Even light that is traveling at the speed limit cannot escape. You just can't go fast enough to escape once you are inside the event horizon, because the speed limit of the universe prevents you from going fast enough to escape. Basically you would be on your way to being spaghetti-fied as you approach the black hole, or maybe not. There is a whole lot we don't know about the inside of black holes, so who knows what could happen in there. There are theories that say that super massive black holes could have different effects on things, but I only know of them and not how to explain them.
Outside of the event horizon, you can technically escape by accelerating away. But it would require so much energy that you wouldn't want to cut it close, I would think.
Gravity does bend space and that does cause light to curve along with space. If there's enough mass, it can bend space enough to essentially make a lens that can magnify light coming from behind. A black hole can bend space so much you can see the opposite side of its accretion disk above and below the event horizon.
If you're interested, I watch a lot of Antov Petrov, Cool Worlds, Dr. Becky, and PBS Space Time on YouTube. That's where I have learned most of this stuff. PBS Space Time can be a bit hardcore sometimes, but they have tons of information.