The tldr is not every species with a uterus menstruates.

Most animals' bodies don't convert into a child bearing state until they're already pregnant. Dogs and cats for example don't grow breasts (or line their uterus) until they're pregnant. Humans (and a few other species) evolved to just be ready to raise a child at any time, which results in permanently developed breasts and a continuous refreshing of a uterine lining.