Because menstruation is so central to human life, we assume it's the mammalian default. It isn't — it's a rarity. Most female mammals build up a uterine lining during their cycle and, if no pregnancy occurs, quietly reabsorb it back into the body. No shedding, no blood, no mess. They recycle. The menstruating species are the exceptions that throw the lining away instead, expelling it through bleeding when the cycle ends without a pregnancy.
The membership of the "menstruation club" is the first big clue to the mystery. These species don't form a tidy branch of the mammal family tree — primates, bats, an elephant shrew, and a desert rodent are not close cousins. That scattered pattern means menstruation didn't evolve once and get inherited; it appeared independently, several times over, in lineages that otherwise have little in common. In evolution, when the same odd trait keeps reappearing in unrelated groups, it's usually a sign that some shared pressure keeps pushing different animals toward the same solution.
So the real question isn't "why do we bleed?" It's "what problem are these particular animals solving that cows and cats are not?" And to answer that, we have to look not at the bleeding, but at what the womb does before the bleeding ever starts.