When I first started using an old C&H, maybe 12 years ago, I sometimes had problems with squaring mats on my mat cutter. After lots of analysis, I found I was sometimes rotating my wrist when I was pulling. Everything was in square except for me, as the operator. If I had unequal pressure, or I rotated my wrist, there would be slight alignment problems.
I now stand at the end of the mat cutter and pull the blade so it is being pulled straight toward me, so my wrist does not rotate at all, and my shoulder, wrist and blade are all in a straight line. I also make sure I hold the bar down at constant pressure. Haven't had any problems in the last 11+ years, now, once I corrected my process.
I now use a wall cutter for squaring mats because I get better productivity; I finally broke down and got a wall cutter about 7 years ago, because I was having problems pulling a score on 40 inch museum glass without rotating my wrist, but it works great on mats. Just cut a straight edge on one side, then always cut the other sides from the straight edge you cut, because mats are rarely square. But even with a wall cutter, make sure your wrist and shoulder are straight in front of the handle; if you are standing so your wrist or shoulder are slightly off to the left or right you will not get perfectly straight cuts.
There was a recent article in PFM [Picture Framing Magazine] about squaring mats.