The modern world revolves around technology and industry, along with products and process that vastly outnumber the [self-centered] people on any one continent. Whatever is more efficient for our machines to work with; that is the language we will all come to speak in the public marketplace.
It is more logically correct to refer to dates in MM-DD form. This is how we deal with things in international standard science (SI units), mentioning the larger incremented scale before we mention the smaller ones (hh:mm:ss). Denominations that change less, like the year, are often truncated. If you were to use those as file names, they could be sorted chronologically by anything that reads the first character it sees.
The name of the weekday is typically mentioned before providing Month/Day because most of the world operates on a repeating 7 day workweek; not because it is correct to start with smaller denominations first. A large part of the world has a regular schedule where the same days are on and off every week for much of the year, and the number of the month is less relevant. This is likely why people started to put the number before the month (i.e. Today is Monday the first). People are not good when it comes to merging previously-learned contradictory systems.
If we operated more efficiently, we would likely say something like October – Monday – 1st. The calendar is a form of data table; when describing a data table we refer to page (header), column (letter), and then row (number). However, people have been dealing with irregular calendar dates for so long, that a more efficient way of doing it would sound wrong to them (October M1, T2, W3, R4, F5, S6, N7). I’m sure if someone tried, they can come up with a fast system that relays all necessary business-world information about a date (like end of month crunch).
When you are referring to a date in a different month, you would make note of the month change first so the person you were conversing with could process it better. This comes from how scheduling is done; while physically using a calendar, you must flip the page to the next month before you begin looking for the date number. There is no reason to state the day followed by the name of the month, unless you realized after the fact that the month needed to be mentioned. If you were referring to the current month, you often assume the person knows it (i.e. Patch day is the 1st).
Dibrom is also correct to point out how our counting system puts the number before the object it describes (5 apples, 1 october). This makes putting the number first an even worse idea; someone starts to process that you are counting objects instead of refering to time.
