The article fails to make the distinction between lunar and solar calender. It's just about dividing the solar year to equal months, but we also want to make the month align with the moon, which circles earth for 29.5 days on average. The big problem with the Gregorian calendar, in my opinion is that it so clearly missed the lunar month. it just feels intolerably close, but not quite there...

by the way, no need to invent a new calendar. the Hebrew calendar is both solar and lunar.