It's easy to look back and wonder what they were thinking, I agree. Temperance advocates had various advantages. There does seem to have been enormous enthusiasm, a deep conviction among the Temperance forces that banning alcohol would save most families from destruction, enable men to lead productive, long lives, and save huge mounts of money ( at a time when most manufacturing jobs were pretty harsh and life pretty hard, it was also easier to point a finger at alcoholism being a cause of so much misery, instead of questioning if perhaps working hours were too long and wages too low). The movement itself was also tied to Christianity ( ergo, The Women's Christian Temperance Union) at a time when perhaps most Americans' social lives, friends, were tied to belonging to a church ( though some churches, like the Lutherans and Episcopalians, were not keen on the idea). But maybe one of the key political reasons was the strategy developed by Wayne Wheeler of the Anti-Saloon League to campaign against any politician who did not toe the line and sign onto the Temperance movement. Once political leaders learned that a stellar record of public service didn't matter to the ASL, that they would try ( and often would succeed) in turning out of office any senator, congressman, governor, etc. who did not vote their way, they were immensely powerful. It was the first single-issue advocacy group: decades later Gun Rights and Anti-abortion groups would use the same technique.

There was also not a very unified, strong opposition.The brewers and distillers didn't really mount an effective counter-campaign, and people who simply liked to drink did not form into cohesive advocacy groups, either.

Okrent: Last Call

Just as a general comment, there are lots of events in history that seem "crazy" to a contemporary observer. One of the lessons of history that for some reason is difficult to stick is that people in different cultures and times had wildly different values from the ones you or I may have. To project our values back on them is a common fallacy and leads to second-hand interpretations that are at odds with the primary sources of the time.

So while the passing of Prohibition might seem incredible to you today, and sparks a natural curiousity to be encouraged, it should also be a good reminder that your answer lies in realizing first that what those people thought and believed and valued was probably just completely different from you, and your answer will be partially in finding out just what those differences are.