Becky, in Month 4, the Pieced Swags are introduced and Sue talks again about "cut parallel to the selvage". I can see the confusion. You want the 1.5" x 5.5" pieces to be as stable as possible, so the lengthwise grain--that is parallel to the selvage--to be along the 5.5" length. So cross cut the strip 5.5" then sub-cut into 1.5" units.
Another HUGE TIP I wish I had known--when making the pieced swags, be sure to backstitch at the beginning and end of each seam. I didn't. and had lots of fixing to do during quilt assembly as the stitches started to open up at the ends of the seams--of course, I worked on it off and on for 8 years so they got handled a lot, off and on. Just get in the habit of securing those seams and you will be really glad you did later.