Ciao Corrado,
This is not easy to explain, because Germany has a federal political system. There are a lot of laws and promotional works on different government levels. A second line working on the cycling network are related to touristic projects. And finally it is a balance of proposals between governmental groups, car lobby (ADAC) and cycling lobby (ADFC).
Todays situation is characterized by:
1. The National Cycling Traffic Plan. This plan from the ministery on the highest government level (Berlin) intends to promote cycling in Germany for touristic cycling routes as well as improving communal cycling for daily use and changing individual traffic preferences. The plan has been considered for 10 years (2002-2012). The money is given to different institutions in the whole republic including scientific researches. The plan is corresponding to the Fiets Masterplan in the Netherlands, which has been sucessfully approved between 1992-1997. The part of cycling traffic on the whole traffic in the Netherlands has increased up to 27 % today.
2. As well as the national plan there are existing many cycling traffic plans in the cities and villages. Larger cities have a cycling traffic planer, who works together with the genereal traffic planers and the cycling lobby (ADFC).
3. The tourist offices of the regions are interest in well accepted sporting activities for getting more visiting and holiday guests. Cycling is popular on all levels in Germany (not only sportive like in Italy or Spain) - mountain biking, racing, family biking, voyaging etc. It's a big market instead reality is a little bit less important. Therefore the touristic cycling network has improved over the last years very well. The same with mountain bike routes. This is done by regional or confederal governments, even of communal governments, too.
Instead of this positive development, cycling in Germany makes a lot of trouble in a political sense. There is still a conflict with car mobility, because a cyclist on a general road or street is not well acceptet by the car driver (less than in Italy). There are not cycling routes everywhere, and not every cycling route is as well as you discovered. Even the money of the plans I described above is not enough for a real closed national cycling network. The budgets of most governments are under the bottom line. So the plans are not still working on.
The main conflict in Germany is the obligatory use of cycling pathes (white sign on a blue background). A lot of caclist want to ride on every road as possible because they have better traffic lanes. And the car drivers want to drive fast and be free of slow cyclists on "their own" roads or streets. The historic reason for this conflict is an answer of your question, too. It was the government of Hitler, which created together with the car lobby in 1934 a law called "Reichs-Straßen-Verkehrs-Ordnung" (RStVO). It was the first time to get free lanes for the cars for driving on "secure lanes, free of cyclists". Cyclists had to follow limited lanes aside the roads. This was the first step for systematic building of cycling pathes. The "free car driving areas" was motivated by Hitlers vision, to show the foreign guests of the Olympic Games in Berlin the "upcoming" Germany - not only on highways, but on all roads, too.
The reasoning for obligatory use of cycling pathes has changed to "for the security of the cyclist". The boom of cycling routes, especially the touristic ones, followed the general cycling boom in the 1980s. Traffic planers were confronted with arguments for a more active life (health) and an ecological world. The political pressure increased to push cycling traffic and cycling tourism.
In opposite to your impression, for me is cycling in Italy, France or Spain easier, because there is only one road system. This cycling network in Germany is a second traffic system, which is in many cases not satisfieing (dangerous, uncomfortable, expensive). Slightly better in Austria and Switzerland, but not perfect, too.
Sorry, that I wasn't able to make it shorter.