Why is it that once you’ve cut paper a few times with your perfectly good pair of scissors, the blades are dull enough that you have a tough time cutting through fabric with them?
My WAG
Many fabrics (not all) require super sharp scissors because they will buckle much more easily than paper which is relatively stiff and can be cut with comparatively blunt scissors. Most paper (as a substance) is harder than most fabrics and will take an edge off quickly although the scissors will contimue to cut paper fine for quite some time because of the aforesaid stiffness. Maintaining a very sharp edge requires fairly specialized steel alloys. The pair of scissors a good barber/stylist uses to cut your hair can cost hundreds and hundreds of dollars just for one pair.
As astro suggested, paper is a much different substance than fabric. Fabrics are soft throughout. Paper is made of little hard, rough bits felted together. Paper needs a “bite” to its surface to make pens and pencils function properly. In one sense, most paper is very fine sandpaper, and has the same effect on cutting edges.
That’s why your mother always got after you for cutting pictures for your report out of the encyclopedia with her good scissors.