Discrepancy is that we're mixing (lunar) months and weeks with solar timekeeping, in a solar calendar. These are fundamentally incompatible, so we've gone with

Discrepancy is that we're mixing (lunar) months and weeks with solar timekeeping, in a solar calendar. These are fundamentally incompatible, so we've gone with cramming the approximate periodicity of the lunar calendar into the solar calendar, while ignoring the fact that we're no longer tracking the moon, and that the weeks don't line up with the year, and the fact that the months are randomly different lengths because they also don't line up and we don't want a weird half-month at the end. Another potential fix would be having two calendars. A lunar calendar for weeks/months, and a solar calendar for seasons/years.