Update:
I was at some BSA (Boy Scouts of America) Scoutmaster training on Saturday, and one of the instructors mentioned that if you have small children don't try to use dryer lint for firestarting because their clothes are flame-retardant....
So maybe that's why I couldn't get the lint to take.
Yeah, using dryer lint is good for learning purposes. However, deliberately packing dryer lint, if you have cotton balls available in large quantities, borders on irresponsible.