GR breaks down at Planck Mass

Question

I have heard a lot of times (see e.g. papers like [1, 2]) that GR is not renormalizable and breaks down at energies at the scale of the Planck Mass $M_{\text{Planck}}\sim 10^{19}$ GeV. What is the (simple) explanation for these two statements?

1. On the possibility of laboratory evidence for quantum superposition of geometries

2. General relativity as an effective field theory: The leading quantum corrections