I don't recall the exact thread you mention but my guess is that they are talking about measuring and therefore cutting from the left edge of the fabric which would be the correct way if you are right handed, I have two left handed students and they cut from the right edge.

You would start any cutting by squaring up or straightening an edge, this is normally done on the 'right hand' side, you would then turn your fabric (or mat with fabric on) so that your straight edge is to your left. You then measure with your ruler or with your mat lines to the point you wish to cut. This gives you a known straight edge to measure and cut from, so you are measuring and cutting from the left but to the right hand side of your ruler. This is reversed if you are left handed. I hope this helps.