In Number the Stars, why did the Danes destroy their own navel fleet?

The Danes destroyed their fleet to prevent the Nazis from getting it and using it in the war effort.

When the Nazis invaded during World War II, Denmark fought back.  Unable to prevent occupation, the Danes opted for clandestine opposition.  The country developed a state-sanctioned underground movement to impede the Nazi war effort, including the smuggling of Jews out of the country.

The next evening's newspaper had told the sad truth. The Danes had destroyed their own naval fleet, blowing up the vessels one by one, as the Germans approached to take over the ships for their own use. (Ch. 4)

Destroying your own war materiel and facilities is a practice known as scorched earth.  If a country destroys its own resources, it prevents them from falling into enemy hands.

When Annemarie learns that the fleet has been destroyed, she comments that the king must be sad.  Her father tells her that he would be proud.  After all, he and his country fought back instead of just giving in.  Denmark was a small country, and the Nazis had overwhelming strength.  They overran much of Europe. 

The incident helps Annemarie appreciate that nothing is simple in war.

It had made Annemarie feel sad and proud, too, to picture the tall, aging king, perhaps with tears in his blue eyes, as he looked at the remains of his small navy, which now lay submerged and broken in the harbor. (Ch. 4)

As the war goes on, Annemarie will have to think about many adult concepts.  Her understanding of the destruction of the fleet is an example of her developing maturity.  War makes children grow up fast.  Annemarie will have to learn many hard truths, and will be asked to make difficult choices.  She is afraid of the Nazis, but she does her small part in the war effort nonetheless.