The enforcement of prohibition on a national scale (as opposed to a statewide level) represented an unprecedented expansion in the federal government's authority. The federal government would have to stop the importation of alcohol (a massive project in and of itself) while also ensuring that its manufacture and sale stopped and stayed that way. This would mean a nation wide policing effort in ensuring that all beer, wine, and spirit producers closed shop and destroyed their leftover stock. Up until this point the federal government had never taken on such a responsibility and it was not clear that the constitution granted the power to do so.

Let me know if I've missed the mark and I shall try to clear up any more questions as best I can.

Sources:

McGirr, Lisa. The War on Alcohol: Prohibition and the Rise of the American State. New York: W.W. Norton & Company, 2016.

Okrent, Daniel. Last Call: The Rise and Fall of Prohibition. New York: Scribner, 2010.

EDIT: Let's get in to the efforts of the Anti-Saloon League (ASL) and the Woman's Christian Temperance Union (WCTU). The Anti-Saloon League, as the name indicates, was initially opposed to the institution that served alcohol rather than alcohol itself. The 19th century saloon was a cesspool of gambling, prostitution, and addiction. Alcohol's direct ties to such a seedy organization helped to perpetuate the idea that alcohol was responsible for societal problems like the spread of venereal disease, loss of family income, and domestic abuse. The WCTU used these points to argue that getting rid of alcohol would lead to a better society.

These were the two most powerful and influential temperance societies in terms of influencing lawmakers and the voting public to consider the merits of prohibition. This is not to say that they were united in their ideas of how to achieve prohibition. Should they focus on individual pledges of sobriety until there was no one left to drink? Bring up ballot measures at the state and local level? Push for national reform? Many members were outright hostile to a national solution, so they pursued action at the state level. They were quite successful. By 1919, 28 states had some kind of prohibition laws on the books.

Then, in 1913, the constitutional campaign was launched which aimed at adding a prohibition amendment to the constitution. This is a stark departure from the previous efforts at the statewide level, and I would argue, that it is because of the success of the Progressive movement in other areas. The 16th and 17th amendments (both passed in 1913) demonstrated that change could be effected nationally in one fell swoop. Similar hopes were held for a prohibition amendment. If the forces of prohibition could win on a national scale, then all lives (so they argued) would be immediately improved without having the uncertainties and the delays that were related to the state-by-state campaign. It also meant that the Prohibitionists did not have to spend their time and money attempting to convince cities (filled with immigrant, working class wets) to give up an integral part of their leisure culture.

World War One made prohibition a reality. As the United States entered the war in 1917 everything was turned over to the war effort. People joined war industries, were expected to scrimp and save their food and ration their other consumable goods so that everything possible could be used to win the war. In such an environment it isn't difficult to see how turning good, bread-making wheat into beer would be seen as a waste of resources and actively damaging the war effort. It also didn't help that most of the companies making the beer bore German names such as Pabst, Busch, and Schlitz. Wartime patriotism fueled the prohibition amendment to success under conditions that were wholly unimaginable before the war began.

In my earlier comment I made a remark that the 18th amendment "was crafted" to address a perceived lack in constitutional authority to regulate alcohol on a federal scale. I was intentionally vague on this point because I felt that it was too difficult to say any one person or organization wrote the amendment. I hope that I have included enough information about the efforts of temperance societies in the 19th, and early 20th centuries to demonstrate that the evolution of their tactics from individual pledges to local and state option laws to full blown prohibition was a factor of their early success and that of the Progressive movement at large.

Sources: Same as above, except I have also taken a look at:

Rose, Kenneth D. American Women and the Repeal of Prohibition. New York: New York University Press, 1996.

Related question: Since the passage of the Controlled Substance Act in 1970, if prohibitation were instated today, would making alcohol a Schedule I drug give it the same effect? How is the 18th Amendment different from the CSA in terms of the political atmosphere in passing it and in how the law was enforced?

Top answer is solid. Another angle is what authority would Congress have to pass such a law? The answer today is the Interstate Commerce Clause, as it is the basis for the Controlled Substances Act. Whereas the constitutional basis for the Controlled Substances Act is not generally viewed as controversial today, the doctrine expanding the Commerce clause to what it is today didn't exist then.

(To clarify briefly, Congress is a governing body of enumerated powers listed in Article I, Section 8 of the constitution. So if a power listed there does not justify the passage of a law then Congress cannot act.)

Wickard v. Filburn 1942, created the "dormant commerce clause" cumulative effects doctrine, which allows Congress to regulate even intrastate commerce if it has a cumulative effect on interstate commerce. The Interstate Commerce Clause was also upheld as the basis of Congress' authority for passing the Civil Rights Act of 1964, which was a major expansion of congressional authority.

Prior to these cases the Interstate Commerce Clause was interpreted as being much more narrowly. In the 1920's it might have seemed that a constitutional amendment was necessary to prohibit a substance outright, even local production which would not enter the stream of interstate commerce. And indeed, it might have been necessary, as the Supreme Court of the time likely would not have upheld it. Doing so would have required the creation of doctrine which didn't develop for more than twenty years after that time.

Edit: Correction. Dormant commerce clause is something else, and is not what I meant to say. Pardon my carelessness.

Follow up. Are there any other examples of such prohibition in the world?

What were some of the social and psychological effects of prohibition?

Was alcoholism a significantly worse problem for society back then?

While alcoholism is a real problem today, it doesn't seem like something of the magnitude that they would ban with a constitutional amendment.