I'm a lefty and have no problem using a rotary cutter.
If your ruler is moving when you cut, they make little sand paper disks to put under your ruler so it doesn't shift.
Maybe your table is too high and you can't get the leverage you need. Try cutting on a lower table. Are you using a 24 inch ruler? Cut only 5/6 inches at a time, move your hand up the ruler where you will need to cut, cut another 6 inch section, moving your hand up to the area you are cutting helps you keep pressure on the ruler where you are cutting, this helps keep the ruler from shifting.