Some words don't have logic behind them. You don't have to think like Germans and I think Germans also don't know the logic behind different compound words. The same with English. What is Missunderstanding? The girl standing downstairs? :)

Once I met a German who told me that he will be at the "Anlage" but I could not figure out what this word means although I knew what the word "Lage" means. 

So better learn each word seperately.

As a native German, I agree with Nacir. Some words just don't seem to have logic behind it. The etymology of words isn't always that easy to guess or know without a deeper knowledge of the language's history.
I personally would (as Nacir did) suggest to learn each word and try to find your own explanation or any easy way to memorize it. Sometimes you'll find a logical explanation for e.g. the prefix of certain words (like the "er" of "erziehen") and sometimes not.
Just look at articles for example. In German we have "das Mädchen" but I won't be able to say why it's neutral.

Lastly I want to say: Yes, most certainly many Germans don't have a clue about their own language and why the language is like it is (except you study German). I'm not quite sure how many adults even remember the cases.....

well because German believed the God, who brought Light, was a woman. She had the name Sól, or Sunna (in Old High German). And she was also the sister of moon God, Máni. Meanwhile, Máni was a man.

Niclas, German isn't the only indo-european language where children of both sexes and maidens are in neutral:)
Of course, they have an explanation... but you can reinvent it yourself. Nothing for sure here.

There was a pretty well known popular book
http://en.wikipedia.org/wiki/Women,_Fire,_and_Dangerous_Things
deriving its title from the categories of words making together an exotic grammatical gender in some Australian aboriginal language. I put it here just for it's title)

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In Russian (i'd never believe that German differs much) we sometimes/usually don't understand clearly the logic behind a word formed some 1000 years ago. And even at the time of formation it could be rather a 'feeling' [a sense of language] then the logic proper that directed it.

But what's true: 1. when you know a lot of cognates and similar compounds you can feel something.

The more curious you are about the language, the better you can describe your feelings.
2. sometimes (may be, more often than we can suppose) we really have some image in our head, associated with the word, or its' literal meaning.
3. sometimes the logic exists and it is clear)

The teacher was right in a sense.... probably.

No, but I've wondered why the sun is feminine and I've concluded that maybe because it's HOT.