Apparently there are about 7 million oocytes created per generation[1], which could be done in 23 divisions: 2^23 = 8,388,608
So first, it doesn't require that many divisions per generation of human. Second, there are "errors" that get passed on to the offspring. Third, a lot of selection goes on so that only fertilized eggs without huge issues will eventually be born.
[1] https://en.wikipedia.org/wiki/Oogenesis
