How could we have so many past lives without reaching some degree of wisdom or enlightenment?

While I do have a personal and intimate belief in reincarnation, I really struggle with the Buddhist belief that we have innumerably many past lives. A monk I listened to explained that all the beings we meet everyday were once our parents in a specific past life, as well as our enemies. Honestly, i find this perspective quite hard to believe. It seems to me that if had so many past lives, we should have reached wisdom and Buddhahood at some point already. How (according to Buddhism) is it possible to have such an accumulation of experience, without reaching some degree of wisdom or enlightenment?