The argument is that writing the parts in a consistently increasing or decreasing precision order makes more sense.
So these are good.
- year / month / day
- day / month / year
And this is bad.
- month / day / year
So these are good.
- year / month / day
- day / month / year
And this is bad.
- month / day / year
Personally, I write the month out if I'm not using 8601 formatting to avoid any ambiguity.
For any sort of recordkeeping, though, I think it's preferable to go full on YYYY-MM-DD. It's more thorough, precise, and sorts properly on a computer.
"May 3" / "May 3rd" or "3 May" ?