Translation:Today is February second.
I agree. Whether or not one way or another is the "correct way" as a facet of English grammar or whatever, Duolingo isn't supposed to test you on your English (unless you're taking an English course lol), the important thing is that the translation is being understood, which it clearly is with or without "the".
For this lesson I suggest this site for better uNderstanding: http://www.omniglot.com/language/numbers/japanese.htm
It has an explaination about how to say the days of a month, for example, february 2nd- Nigatsu - 2nd month, Futstuka - 2nd day of the month
There are at least these three ways to express dates in English. For this example. February 2nd. February the 2nd. The 2nd of February.
Whether the article "the" is included is not a matter of spoken v written, but rather how the expression of the date is connected in a sentence. Examples:
The 2nd of February is my birthday. vs February 2nd is the date of my birthday.
In the latter, "the" before "date" produces a sort of redundancy for definite articles going before "the date" and are thus omitted. The same occurrence can usually be observed in structures containing related particles such as "on."
Oh dear, another USA vs the English speaking world debate! Trouble is, it is very hard to ignore when you've spent your life hearing it one way. Order is also different throughout the world. Month, Day, Year. All the computers say it so it must be right! Except everyone who has Day, Month, Year in their upbringing, or Year, Month, Day. I'm actually puzzled if anyone except the USA doesn't use hierarchical nomenclature?