Whew, fun one.
There are a few answers to this one. There's the celestial gears model, which essentially models the gravitational influence of the stars as interlocking gears, so as one rotates the other rotates in the opposite direction. I just can't work out any clear way for the stars to be distributed between 'gears,' to get rotation around two points but that's one explanation.
The other explanation is in DET. a less-accepted model, but still. At a basic level, the idea is that the Earth is a two-sided disk, the edge being at the equator, so that you could easily get stars rotating above two points, one above and one below.
There's a whole host of things to say how the crossing of the equator works (though if you assume it's possible to cross, then the same would hold for light so we would observe stars rotating about two points near there), there's an explanation it's just quite a long aside for a question on a different topic.