This doesn't just happen in Berlin. I've lived in several German cities, Berlin included, and it's really difficult to find an apartment in _any_ reasonably large/popular German city (e.g. Hamburg, Frankfurt, Munich, Köln).
It's a Germany-wide problem, that just happens to be most acute in Berlin. Unless you're really fast, super aggressive, or can leverage your network to talk to the people moving out, you'll have a difficult time in finding an apartment.