I've read that female mules can sometimes have offspring, but that male mules are incapable of doing so. Why is that the case? Is their sperm not capable of entering the egg or is their a genetic reason?
It's essentially genetic. The mule is a hybrid of a male donkey and female horse. A donkey has 62 chromosomes, a horse has 64 chromosomes, and a mule has 63 (mix of 62 and 64). There is a mismatch between both number and structure of the chromosomes and as a result, most mules are infertile.