Also, I don't know how it's in Germany, but in other parts of Europe, your employer can force you to take your vacation days. Most do it at the end of the year, because if you have unused vacation days and you quit, they have to pay you extra for the vacation days you lose by quitting. And as you noted, sick days aren't counted in that. In fact, I can take a one-day sick leave whenever I want without so much as a doctor's notice (company policy mainly due to the fact that taking a sick leave with a doctor's notice creates more administrative work which isn't worth it for a single day).
I don't know either if your employer can force you to take your vacation. But I heard that your health insurance may deny benefits for stress related issues if they find out that you didn't take all of your vacation days.
Here in Poland he can force you, and often does, because if it is found out that employees didn't take all of their vacation time the company can pay a substantial fee for that.
