> Still only 2% of men take the leave, while 42% of women do [1].
  > I can only speculate as to why.

This is actually pretty simple: Germany's culture is still deeply rooted into old gender roles - father provider and mother educator.

To give a context of the culture and legal system, as of today, unmarried fathers don't get legal custody automatically, and if they apply and the mother refuses, they need to go to court. This is even a recent change; until 2009, if the mother refused, there was no chance, and until 2013, the father had to go to the European Court of Human Rights.

Germany has a very surprising family culture in the Northern Europe context - the surrounding countries are considerably more progressive. An educated guess is that the Nazi regime promoted the father provider/mother educator model, and it's taking a very long time to move on.