Dating culture in Germany:
Two people meet and get to know each other.
While Americans are largely fine with meeting a stranger for one hour before arranging a date, Germans prefer to take much longer. They prefer to meet through trusted circles, to get to know someone for longer, typically through groups of friends, before developing it into something romantic. This is one reason why online dating is slow to take hold in Germany.
If a German woman accepts an invitation to meet alone, she will/may NOT interpret this as a "First Date" or a clear indication of romantic interest. She will/may think of it as "Getting to know this person better".
At some point, from this process, two Germans will somehow become a couple. Commonly, groups of friends who know each other over long periods like to party together, and eventually people simply pair off from the group. One drunken make-out (within a group of long-time friends) often creates a couple.
While many Americans date numerous people at the same time before going exclusive, Germans find this offensive.
Funnily enough, online dating is introducing some concepts of US-style dating to Germany. Online dating is big in the US, but it only changes step #1 of the dating process: meeting and exchanging numbers. After that, dating is the same as it's been for decades. But since Germans never really HAD a dating culture, online dating is introducing them to the whole dating concept.
For Americans, a date is no big deal. It's low commitment, you can leave any time, and never see this person again if you don't want to. That goes completely opposite to almost everything in German culture. Germans let few people in personally, but once you're in it's for life. They are polite people, and may not feel comfortable asking for, accepting, or declining a date invitation, because not everyone agrees what the expectations are.