What ? This is not true at all. Menopause is present in all mammals. The reason you don't see it in most mammals is simple : the normal maximum age for most mammals is less than half of humans. Most animals grow to about 30-35 "dog-years", and die. Dogs and cats in captivity, some long-lived races, do experience menopause. If humans died at 30-35, which is about the expected age for humans in the natural habitat, it would be a very rare woman indeed that experience menopause. (Keep in mind that 35 is the average age of death for humans in nature. But at that age most deaths are still accidental, meaning there is a large deviation. A lot of kids would "naturally" die 5 years or younger (like 30-50%, depending on environment), then there is a certain chance of dying every year. IF a human can avoid nature, infection, fights (or you know, win them all), poisoning, famine, ... a male human would age to about 40-45 years in nature, a woman a little older. But no more than 2% or so will ever see their 45th birthday in a natural human population)
Here's the key, when a female baby takes her first breath (oxygen in the lungs), a mechanism is set off that causes the ovi to cut off all connections to the mother body. To put it simple: before a baby girl takes her first sip of mother's milk, all the baby's children have become independent lifeforms, no longer connected to the mother's body. The baby's DNA will sabotage and boobytrap it's own ability to create new ovi at that point. This of course means, among other things, that their numbers are 100% fixed at this point. This means that at that point the number of fertility cycles her body will go through is a constant from that point forward. There is a similar, but more complex, process set off in men (in men, too, the cells that form the reproductive cells are very isolated from the rest of the body).
When a human is disconnected from the umbilical, a number of changes happen as a result of that in order to switch to what you might call internal power if it were a robot. The immune system wakes up. The lungs inflate. The heart starts actually pumping blood around (yes it beats in babies, but a baby would survive without a beating heart as diffusion will actually happen fast enough. This is really sad when it happens since the baby is alive at that point, but growing will kill it). Cell reproduction rates are massively cut, and are moving towards replacement-only (a 2 year old is -almost- no longer making extra tissue. An adult is simply a 2 year old with "stretched" cells, not more cells)
Essentially nature is trying to protect the next generation from DNA alterations by external influences. Menopause is just a side-effect that evolution doesn't care about because women are unlikely to have viable children at that age.