My God, I just spent half of the last night debating this on Facebook -.-

My takeaway from that experience - when someone struggles with understanding why those two views are both equivalent and OK, make sure they understand this thing: heliocentric and geocentric models have only one purpose. They let you compute where planets will be at any given time. They do not try to answer why the planets are moving the way they are. For that, you need at least Newton's model of gravity, which actually doesn't differentiate between the Sun and planets at all.

Geocentric models still pop up in real life. When you're using a sky map to determine where some planet will be visible tonight, you're looking at a geocentric representation.