Many if not most of these oddities about humans come down to either they don’t affect reproduction, or because humans are social animals. Menopause makes sense because a grandmother will have more successful descendants if she stops having babies and helps her daughters with the grandkids. I would guess the few other species that exhibit menopause are also social animals.
A couple more points to add to this:
Most species make a baby (or babies), raise them to maturity before having another. Even a low chance of successfully raising another child is advantageous over no chance at all from turning off the baby maker. Humans, however, have children of a range of ages, making more before the first is finished. Having another inherently takes away from the ones that already exist. Having another that probably won't make it can be an evolutionary negative.
And humans have a much longer portion of their life spent on each offspring. This increases the chance of death before completion and thus makes more evolutionary pressure towards not putting effort into futile things.
Note that this works even if she is alone and doesn't help with the grandkids.
This is discussed at the bottom of the article: "Menopause: Humans, killer whales, pilot whales, beluga whales, false killer whales, narwhals one group of chimps in Uganda. No menopause: Everything else"
So, monkeys and apes (besides one species of chimps) don't get menopause, elephants don't get menopause, lions don't get menopause. If your prediction is, social animal => menopause, it's wrong 99% of the time.