If you and your friends took some helicopters to the north pole and went up and then took off in different directions and flew at the same altitude you would feel like you were being bent towards each other, but yet as you all started to approach the south pole you would notice that you were all moving a way from other at first, you were all moving parallel at the equator and you were rushing together as you approached the south pike.
None of you felt like you were being pulled together. But yet the curvature brought your diverging paths together. Same with ants crawling down a disco ball suspended from the ceiling. Curvature does that.
But gravity does that too. If you and a million of your friends all took rockets straight up to check out the satellites all at the same time and then all decided to skydive back down to earth at the same time then as you are each pulled straight down towards the center of the earth by gravity you'd feel the brush straight down but as you get closer the million of you are distributed over spherical shells of smaller and smaller area so you end up getting closer and closer together even though you were all pulled down and not being pulled towards each other.
And also you all move the same way, regardless of how massive you each are. Same with he helicopters going from north pole to south pole. And same with the ants crawling down the disco ball hanging from the ceiling.
This is an inspiration that maybe the reason things starting out parallel get closer and do it the same way regardless of how much mass is that they are just moving on natural oaths in a curved space. And actually time has to be curved too. Even if you fire your rocket engines to stay at rest against gravity, your clicks tick faster farther from a planet or a star.
OK, so we want things to be curved because that explains things. And that wasn't precise enough, Einstein had to make highly specific about how exactly it curves. And actually the math just describes how clocks and meter sticks work in different places and different times.
The idea that spacetime is curved is the interpretation that fits the math. The interpretation doesn't need another interpretation.
And empty spacetime can be curved, stress and energy and momentum and pressure just can make it curve differently so can help the curved spacetime in the vacuum to grow bigger and stronger.
In general (I mean most commonly), matter collapse and creates more curvature in the vacuum where they used to be (and even make more space where they used to be) and in exchange can acquire energy. That energy can be given to other things in a way where you can't get it back (for instance radiating heat out to space) and thus we are stuck with the curvature. At least more often than you destroy it. That's why we live in a world where the space between galaxies is curved and he space around a galaxy is curved and the space around a star is curved and the space around a planet is curved.
And it's all spacetime that is curved (not just space). But the curvature is the interpretation.
As long as you predict the way clocks and meter sticks work, maybe you have a weird fields that affect how clocks and meter sticks work. Other interpretations are fine as long as the predictions are good.
But if it loons like a duck and quacks like a duck, people that are am ready familiar with ducks and spent years learning to recognize and predict how ducks behave are probably going to call it a duck. And if really it is a robot that looms and acts like a duck, it doesn't even really matter if it looks just like one and acts just like one.
So I don't see the point in speculating that it isn't curved. Or course the irony is that went spacetime is curved, things move in natural ways, like the helicopters going from the north pole to the south, they didn't feel pulled. If you made a flat spacetime version (which some people have done, and even made ones that reproduce all the known and tested results) then the irony is that in the flat version things will be moving in curved type paths.