There are a few exceptions to this rule. For example, some species of bats and elephant shrews do menstruate, shedding the uterine endometrium through the vagina. However, their menstrual cycles are much shorter than those of humans, typically lasting only a few days.
In general, menstruation is not essential for reproduction. Most mammals are able to reproduce successfully without it. In humans, menstruation is thought to have evolved as a way to ensure the shedding of the endometrium, which is necessary for the implantation of a fertilized egg.