Why were women active in the crusade against alcohol?

The crusade against  alcohol was a protest by women, in part, of their lack of civil rights. Women could not vote. In most states women could not have control of their property or custody of their children in case of divorce. There were no legal protections  for women and children, prosecutions for rap were rare, and the state-regulated "age of consent" was as low as seven. Most local political meetings were held in saloons from which women were excluded. At the end of the  19th century Americans spent over a billion dollars on alcoholic beverages each  year, compared with $900 million on meat, and less than $200 million on public education.

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