Have you ever looked at an image of a quasar host galaxy? See, for example this link. If these are not at cosmological distances then there is a completely new type of galaxy that is very different than every other type. When you look at these images you can sometimes see fully-blown spiral galaxies, If these are not at cosmological distances, and are at local distances, then they are very, very small. And then you have to explain why the redshift-distance correlation should not apply to these galaxies like they do for other local galaxies.