There are a few different answers to this that all kind of build up.

• The original DEA was remnants of the defunct prohibition task forces after the repeal of prohibition; around that time some crime was committed by someone (who, if memory serves, was some form of minority, because of course in America we'll choose to galvanize against a minority) who happened to be high, and they used that as an excuse to make the drug illegal.

• The real push for it came under the Nixon administration, as a way to put his political opponents (and again, minority communities) in jail when it wasn't legal to arrest them just for being black or hippies. One of the higher-ups in Nixon's cabinet has since admitted this in an interview in 1994 that was republished around 2016; to writ:

"The Nixon campaign in 1968, and the Nixon White House after that, had two enemies: the antiwar left and black people, You understand what I’m saying? We knew we couldn’t make it illegal to be either against the war or black, but by getting the public to associate the hippies with marijuana and blacks with heroin. And then criminalizing both heavily, we could disrupt those communities; We could arrest their leaders, raid their homes, break up their meetings, and vilify them night after night on the evening news. Did we know we were lying about the drugs? Of course we did."