In Dutch, the original meaning of those articles has long gone, that's why Dutch is such a hard language to learn.
For instance: It's "de vrouw" (the woman), but also "de man" (the man), so there is no real distinction between male and feminine words. For plural, "de" is always used: "de vrouwen", "de mannen". The article "het" is used for neutral words, but who can tell me if "deur" (meaning door) should be m/f or n? In this case, it's "de deur".
It gets really confusing with words that have different meanings and use different articles for those different meanings.
"De wiel" means a lake which is a result of a hole in a dike (how typically Dutch).
"Het wiel" means a wheel you can put on a wagon.
We only see the original genus of the nouns if we use possessive forms (his, hers, etc), then we can see what it's supposed to be.
Dutch people know that it's: "Ik sluit de deur, ik doe
hem dicht." (I close the door, I shut
him, translated literally).
So Dutch is a language that we learn mostly through our parents and social contacts, more so than on school. The use of articles is very confusing to people who are just learning to speak Dutch and they more often than not do it wrong. This makes it very easy for us to spot foreigners.
Oh, and the story of Hansje Brinker with his finger in the dike is made up just for American tourists.