Earlier quoted context omitted.
I have a much simpler explanation. Most people can't afford it. The median income in Germany is ~44k/yr. If we assume the woman earns a bit less, we can already see why it's more common for the mother to take the paternal leave. It's less of a hit on the finances. If the dad takes it, or both, they might not be able to sustain themselves for long.
If I imagine the women earning a bit less, I imagine them getting 65% of less. Whoever of the parents is earning less, in most cases it would make more sense for the less compensated parent to just switch into part-time, if he/she isn't already working a tax-free "mini-job", while the higher compensated parent takes the leave. This yields the highest income per hours@home.
But that's usually not what people optimize for, they optimize for max total income, because rent or mortgage payments etc aren't based on a percentage of income but fixed amounts. Sure, it's great if you only work one hour a month and get 1000€ for that instead of working 100 hours and getting 4000€. But if your rent is 1100€, what good does that do?