Sure ’nuff, that looks different from the cow leather strops I started with (are they maybe kangaroo?), so I have to accept your description at face value. That said, all of the splits look just like the cuts I experienced when I accidentally went “edge leading.” It can also happen where you try to make long, diagonal up-strokes on long blades. Although you fully intend to make a continuous upward stroke, the fact is that anytime your strop stroke approaches horizontal, you’re likely to slice the leather. Better to make a number of vertical-up strokes with each pass. FWIW, I found I could continue to use the strops, even with the damage I inflicted on them. If a flap refuses to cooperate, just cut it off. If you can, you might try gluing the flap down into its intended position. For leather, the best thing I’ve found is an adhesive called “Shoe Goo” – an incredibly tuff silicone. I have a pair of hunting boots I wrecked by sitting on one foot while roofing my garage in 1985. The seams alongside the laces failed where the thread were worn through. Fixed it with Shoe Goo and the boots are still serviceable.
I will try gluing them down before I order another set. On that long kitchen knife I shouldn’t have bothered with the strops. Oh well…live an learn. Thanks for th info and advice.