Probably because fated is the wrong word they used towards fated pairs. Maybe its not really fate that decided it. At Kashikomarimashita, Destiny, the doctor at the second story suggested that being fated pair is just a matter of body compatibility. He even made the other omega compatible with the alpha in the second story to make it look like they're fated although they're not (maybe through experimenting)
(if you havent read it, i suggest reading it. Its a happy ending (both couples had child))
The first couple is alpha x omega and the second is alpha x beta (honestly i like the second couple more than the first one because before the alpha and beta become an official coulple, so many emotional things happened (especially about the beta being naive towards his feelings and his insecurities of the alpha finding his fated pair. He also doubt himself if he can give happiness to the alpha))
I REALIZED THAT PEOPLE MIGHT BE HAPPY EVEN IT IS NOT FATED, IT IS REALLY DEPENDS ON TYE PERSON HOW TO FACE THE WORLD