The truth is, the Earth's axis doesn't flip1 (only its orientation in relation to the sun changes), and you can balance an egg on any old day. It happens that standing an egg or broom is one of those things that is just difficult enough to do that, when pulled off, people attribute it to some sort of irregularity in local gravity or God being extra helpful. Days like the equinoxes are picked because people love the idea "balance." Ahh, say it with me, "Balance." Now imagine it in a meadow with flowers and people in flowing clothing. They all have yoga mats, too. Sometimes other astronomical events are arbitrarily picked to be "egg balance days." I'd love to hear the solar storm explanation, that takes some imagination.