Dogs in heat, rutting stags and cats in season: animals make it very clear when they’re most fertile. Sometimes this involves a bit of blood. With humans it’s exactly the opposite.
All mammals have a menstrual cycle. But most of them have a covert menstruation. This means the endometrial lining is so thin; it gets completely absorbed by the body if the egg isn’t fertilised. Humans, primates and some other mammals (bats, African elephant shrews and certain tree shrews) have such a thick endometrial lining that part of it is being shed through the vagina.
The bloody discharge you see in female dogs, and sometimes also in cows and species of the horse family, has to do with the ovulation: blood vessels in the vagina wall burst because of the blood pressure. This bleeding is no menstruation. Besides, animals can be quite moody when they’re fertile. Just ask any horse owner with a mare in the stable.