First off! I am new to the boards here and am excited to get started. I have been practicing sewing straight and can see the error of my ways....two things. Too fast and cutting fabric crooked.

Okay, so I have only begun sewing in EARNEST over the last year. I am not very good at it but I think most of my errors lie in my failure to cut fabric straight! I have attempted to use scissors, rotary cutters,rulers, pattern weights, pinning fabrics, tearing fabric -- you name it. My main question is this: I see everyone on YouTube and Jenny especially using a rotary cutter lickety STRAIGHT split and I cannot seem to get a rotary cutter to cut through a piece of fabric without my having to rock back and forth, causing it to shred and cut crooked the single piece of fabric and still 99% of the time I haven't cut all the way through the fabric the entire length, even if I stop to adjust the pressure as I go along. I am just attempting to cut straight lines at this stage of the game and cannot do it. I first thought it was the cheap brand rotary cutter I was using, so I spent more money and purchased the premium Olfa brand, but I have seen Jenny use my "cheap" brand on here several times without having to go back and re-cut or use scissors to get a cut all the way through. I am using a cutting mat (self healing by Olfa) and even pressure, even had dh attempt to use it thinking I wasn't pressing hard enough and he cut into my board the entire length of fabric cutting and STILL DID NOT CUT THROUGH THE single thickness of 100% cotton FABRIC! What operator error does anyone suggest next?
Help!