The singularity is a prediction of GTR, but GTR breaks down there too. This is why black holes are so exciting in the context of new theories which are complementary to GTR!
It even preserves relative motion ! If A and B are both falling towards the event horizon, their relative movement doesn't change : by that I mean that if it was 2 moons, and someone launched a rocket from A towards B, it would take, say 10 hours to get to B. When both fall towards the black hole that time can still lengthen from the perspective of someone standing on A or B. It can shorten. It can stay the same. Depends on how it was changing before they started falling in.
So it could simply be that relativity stretches the space time near the event horizon enough for everything to fit in there, like that tent in Harry Potter. It looks weird from the outside, but if you're falling into the black hole it's the opposite: everything outside of that (very, very large) space near the event horizon is what looks weird. But if the black hole is big enough, it looks weird, but ... not very much.
The entirely weird thing is, you can choose initial conditions where all distances lengthen proportionally, in fact that's the more common scenario. So for all objects that are falling into the black hole, and objects not falling into it, all distances lengthen. Make the black hole big enough and the difference between things falling into it and things orbiting it or even moving away are very very small indeed.
And now you look at our universe, and that's exactly what you see. The value of the cosmological constant (ie. the universe is expanding, but ever slower and it will never actually stop expanding) can be explained by the assumption that we're falling into a very, very large black hole.