Thank you all for your replies! I think the first thing I'll do is get a new cutter. Whenever I see someone cut in videos, the blade just slides through the fabric. I bought mine at Joann's (not Fiskars, not Olfa, it's blue), and from the beginning have not liked it. No matter how hard I press down, it never cuts a line in one going. After a short time it looked like it left little pieces of fabric uncut, as if there were a nick in the blade. I bought a new blade for it, same problem. Maybe it's just a poor quality cutter. And that's why I have such a hard time holding the ruler down, because I have to press so hard on the cutter.
Thanks again!