@bomberfox More:
The reason we get this is because we understand the sums of infinite series. To get somewhere, you have to go halfway, first. Then halfway again. And then again, and again...
If you did not understand sums of infinite series, you might say one can never "go" anywhere, because they will never arrive. They always have to go halfway first.
But if you do understand those sums, you know that 1/2 + (1/2)(1/2) + (1/2)(1/2)(1/2) +... = 1. So you always arrive at your destination.
The same applies for watching someone fall jnto a black hole. If you watch that happen, you will never, not ever, see that person cross the event horizon. Not even if you had an infinite amount of time to observe it.
However, to the person falling in, nothing special seems to happen at all.
So if I asked you what the person who fell in looked like to you "after" falling in, that question would have no meaning. Like asking what is north of the North pole.
(If i asked the person who fell in, they could just grab a mirror and describe what they see. )
So the difference comes down to your frame of reference. For those "inside" of our universe (frame), it seems likely we could go back in time forever and never reach a beginning. But to an observer outside of our universe, they may just see the beginning of our universe occur in their own real time.