I'm not a physicist, just a layman interested in this topic. So, if you're looking for very rigorous explanations, I can't help. That said, my understanding is

I'm not a physicist, just a layman interested in this topic. So, if you're looking for very rigorous explanations, I can't help. That said, my understanding is this: if you try to calculate the trajectory of small particles using the equations of GR, and then compare that to measurements, you'll find that GR is dead wrong. Conversely, if you try to calculate the motion of stellar objects in strong gravitational fields using the equations of QM or QFT, you'll again get results that don't match observations at all. Further, for more complex mathematical reasons that I can't personally follow, if you just try to introduce the GR space-time deformation terms into QM equations, you can't compute anything because the equations diverge.