1) The density of the core approximately matches that of high pressure Ni-Fe, but is way denser than solid oxygen (roughly 1.4).
2) If the core was oxygen then the overall elemental abundance of the Earth would be nothing like the elemental abundance of anything else in the Solar System (or anywhere else in the known universe).
3) The elemental abundance in meteorites, thought to be left-overs of the original accretionary disk, closely matches Earth with an Fe core - doesn't resemble in any way any supposed metallic oxygen core.
4) The seismic data works well if we assume a liquid / solid iron core. If the core was solid oxygen, then the P-wave shadow would be configured completely differently, because seismic refraction at the core-mantle boundary would bend to make shallower refracted waves, not deeper.
5) A metallic oxygen core would could not explain the Earth's magnetism.
6) It would be bizarre for an oxygen core to have evolved when there are much heavier elements in the mantle.