I'm currently finishing my Master's thesis about the "War on Drugs" so I'll be happy to give you my two cents. Although /u/KyleBridge refers to another thread covering the same question(s), that one focuses (among other things) on the paper industry. My own paper is more concerned about the overall chronology of the "Drug War", as well as its moral background.

First of all it's necessary to remark that the Congress didn't prohibit cannabis per se in 1937. Rather, it delegated the responsibility for the taxation of cannabis in 1937, to the IRS.

"it [Marihuana Tax Act red.] technically did not make marijuana illegal; it simply placed a huge bureaucratic burden – with severe penalties for noncompliance – on anyone who wanted to sell or buy the drug." -Reznicek,2012.

The literature concerning this topic attribute this factor to two aspects of the "Drug War". Firstly, by making the taxation and regulation vis a vis cannabis a question about revenue collection, the actors who supported prohibition and/or regulation of cannabis, were able to omit a discussion about state rights contra federal rights. By making the regulation a federal "sized" matter, they increased the scope of their agenda.

"By basing their efforts on the federal government’s constitutionally assigned revenue-collecting powers – that is, on the power of taxation – and on the regulation of interstate trade, proponents of antinarcotic legislation avoided the questions of individual states’ rights that were broached by any attempt at the direct control of drug sales and use." -Hickman 2007.

Secondly, prohibitionists felt that a taxation came across as a more "neutral" initiative, and in this regard "sold" the idea to the congress.

Your question also implies the alcohol prohibition (18th Amendment) which ended four years earlier. This exact prohibition left several without a job in 1933 when (alcohol)prohibition ended,when that the substance they had sought to combat, once again became legal. In comes Harry Anslinger, who was also occupied with the alcohol prohibition earlier. -Bertram, 1996.

Anslinger managed to "spin" the regulation of cannabis in a way, that it was mostly connected to minorities, primarily Mexican immigrants. The immigrants became "persona(s) non grata" since the Depression made them unwanted competitors;

”The consumption of marijuana, or cannabis, in the United States followed an influx of Mexican immigrants in the early twentieth century who were fleeing their country’s civil war. During the Great Depression, massive unemployment increased public resentment and fear of Mexican immigrants, escalating concerns about the problem of drugs." -Reznicek, 2012.

It is also worth noting, that the "Marihuana Tax Act" 1937 was but one of the many chapters in the "Drug War" or "War on Drugs". From a legislative point of view, it expanded on an earlier act known as the "Harrison Narcotics Tax Act" from 1914. The Harrison law (named after a New York Senator) also taxed certain drugs. However, it was only concerned with heroin, cocaine, and opium.

Hence the 1937 act addressed this by including cannabis as another substance to be taxed and regulated. This regulation did not mean a de jure criminalization, rather a de facto since it was not worth paying the taxes and deal with the ensuing bureaucracy.

This is just a brief answer to your question, but I hope you made something out of it. If not, please let me know, and I'll go more into detail with various factors, particularly the ethnic and racial background for some of the regulation/taxation of the various laws. Now, I better finish my paper, he he.

Source(s):

Reznicek, Michael J. "Blowing Smoke Rethinking the War on Drugs without Prohibition and Rehab", Rowman & Littlefield Publishers, 2012.

Hickman, A. Timothy. "The Secret Leprosy of Modern Days" University of Massachusetts Press, 2007.

Bertram, Eva. "Drug War Politics - The Price of Denial" University of California Press, 1996.

Also, why does it seem like the rest of the world followed suite? Were they all taking a cue from the US? What explains the global prohibition phenomenon of the 20th century?

You'll find an answer in this thread.

One last note might be that rather than hoping to stop use, the intent was to target growing minorities. Alcohol had been focused against newer Catholic immigrants, which lead to a lot of conflict between European immigrants and second wave nativist protestants. However, marijuana was linked to stopping blacks and Mexican Americans, which was an easier sell.

Kind of a follow up to this: was there any push back on this new prohibition where they cited the failures of alcohol prohibition?

Related Sub-question: Could it be anything to do with the great depression?

As an additional question: how much did Joseph McCarthy's anti communist efforts play into the effort to prohibit?