Why can't we see anything fall into the black hole?

[Sarcastic14]

Flicking through quite a few topics here, I have seen that everyone says we can't get to see anything fall into the black hole as it would take ∞ time for us.

Now, I'm a bit bugged here. Can someone explain me why it is like that.
Also, haven't we seen stars fall into black holes through telescopes and similar?



P.S. I know I probably don't know the basics here, but I want to learn, so please tell me why is it like this :)

 

[Polyrhythmic]

I'll try with a simple explanation: in flat space (far away from the black hole) we have light cones with an angle of 45° from the horizontal space axis. Now as you get closer and closer to the black hole, the curvature of spacetime makes the light cones bend inwards, which basically means that at some point the angle will be 90°. At this point, you won't see light escaping anymore. for angles between 45° and 90°, one can see from the light cones that light will take longer to get away from the black hole. This time asymptotically goes to infinity.
This explanation is far from complete and mathematically rigorous. If you want to learn more about it, you should start studying some general relativity!