You may (possibly?) be 'tilting' the rotary cutter onto it's side juuuuuust a weeeeee bit.
Get a 'June Taylor Shape Cut'. Get the largest one eventho it is a few dollars more. You will not regret spending those bucks. I promise!
The June Taylor Shape Cut has slots in it for you to run your rotary cutter through. The long rulers never fail to slide (for me) and I just can't get a straight cut using them. Just can't!.
Stand your rotary cutter blade straight up. Practice on scraps or aliminum foil (sharpens your blade at the same time). Watch your blade as you cut and you will see when it is standing the way it was designed to.
A second thing you can do is be sure you have the rotary cutter screw tightened enough to hold the blade but not so much that the blade won't roll when you are pushing it across the fabric.
Another thing is the lint that builds between the blade and cutter. Take it apart every now and then, kleenex the lint off and put a drop of machine oil on the round part of cutter where your blade (lies?) lays. (You can put it on that part of the blade instead but don't cut yourself. Extra careful!).
Can't wait to hear you got the hang of it./Regards, Dorothy