First. So the explanation goes, during the earthquake power substation transformers and fuses blow, causing these lights. Problem is, the grid doesn't sustain that level of damage during these earthquakes. Yes, the power usually goes out and there is grid damage, but the amount of damage is nowhere near 'every substation blowing', even in the most severe quakes. So the number of lights and number of grid faults do not equal.

Second. Earthquake lights present in the sky, not on the ground beneath them. If substations were blowing and creating light, they would light objects in their immediate vicinity (e.g. buildings) more than they would illuminate clouds. But that doesn't happen, and in fact the lights appear within the cloud layers themselves rather than appearing as a projection onto them, as they would if the light source was at ground level.

Third. These lights have been witnessed out to sea and over offshore islands, where there is no power grid.

That last point is the most compelling for me, because I personally witnessed earthquake lights, less than a year ago, offshore, during the November 2016 7.8 Kaikoura earthquake. During that earthquake, I had this (night time) view: https://imgur.com/a/Nt2wD

Edit: It's also been reported around the world that these lights can occur days, even weeks before an earthquake happens.

There's a lot of different explanations for it, but I understand that it's never been definitively explained.

The idea of "Earthquake lights" is also a theory, but it's becoming increasingly more likely these days as evidence piles up.