Because the month is bigger and provides more context on it's own. You figure out the month first then place yourself within that scale.
Example:
"It's May (immediately tells us the context of 31days, spring, etc.) It is the 30th, so there's one day left in May"
Vs
"It's the 30th (provides no context except that it's not February). it's may, so there's one day left in May"
So both lead to the same conclusion, the first way just gives the limiting parameter/most context first.
Similar reasoning why the month is the primary separation on calendars.
Another example that follow this same principle, you tell time HH/mm to provide the larger context first, not mm/HH.