Of course, there is no way to know for sure why anything like Prohibition happens. We can only make informed guesses.
I would argue that the movement for Prohibition succeeded because of the rising power of the middle class and the increasing worries that people had about immigrants.
The main push behind Prohibition came from the middle class. This class was booming during this time and was behind many of the reforms of the Progressive Era. The middle class was notably worried about the behavior of immigrants. They identified alcohol with immigrants, crime, domestic abuse, and other bad things like that. Because there were so many immigrants coming to the US during the late 1800s and early 1900s, the middle class was quite worried about them and their influence. This became even more true after WWI since alcohol was tied strongly to the German community (most brewers were German, for example).
Thus, the rising power of the middle class and the rising concern about immigrants made it possible for Prohibition to succeed.