It's not flipped left to right, but inverted along your axis of vision, which is equivalent to an inversion left to right and an 180 degree rotation. What's interesting is that your eye chooses that interpretation, rather than the actual inversion, or a vertical inversion (you can see a vertical inversion without a rotation with a ceiling mirror, but rotate that upside down image around the left-right axis and you'd get a normal mirror image). Probably because people spin all the time, but they don't often flip or somersault, and we're mostly symmetrical left to right.