1) Because of the Second Great Awakening (1790-1840) and the Third Great Awakening (1850-1900), the American people became increasingly religious (yes, that’s possible), and the religious fervor translated into a zeal to improve the society, and one of the greatest scourge these religionists see is drunkenness (and people back then drank A LOT considering how cheap hard liquor was back then). These people just eradicated slavery, and they were moving down the list of societal ills.
2) Because of the Woman’s Suffrage movement, as married women and children were one of the people most heavily affected by drunkenness (i.e. husbands drinking away all the money, spousal/child abuse under the influence, etc). Prohibition has great popular support amongst the women of America. And as women’s political rights increased, so did the power of the prohibitionists. In fact, one of the Suffragette’s main arguments was that it allowed women to escape drunken husbands.
3) The alcohol trade was heavily involved in governmental corruption scandals (in part because they tried to fight the prohibitionists), and so reform-minded progressives (who were in favor of increasing governmental regulation and oversight) increasingly allied with the prohibitionists against a common enemy.