The point of that line of reasoning is not that drugs should all be legal; rather, it is that the current laws are not based on health (and the assumption is that it should be). Drugs that pose some of the most serious health risks, alcohol and tobacco, are legal and can be purchased without consulting a doctor, even by people who are killing themselves with their habit. Drugs that pose less of a health risk like marijuana or psychedelic mushrooms are completely banned. Moreover, illegal drugs, like illegal alcohol, have unknown doses and may have unknown impurities, or may even be a different drug than what the seller claimed.
Anyone who knows the history of the war on drugs knows that public health is a cover story. The first drug laws in the USA were bans on cocaine and heroin, and the arguments presented to Congress and the general public were overtly racist. It was said that cocaine turned black men into murderous demons who could not be stopped even after being shot in the heart. Heroin, besides being made by a German company, was also said to be popular among Asian immigrants who were bringing their awful habits here. Then marijuana was banned, because, according to the testimony given to Congress, it fueled jazz music and caused white women to want to have sex with black men, and Mexicans were using it to corrupt the white youth. Drug enforcement has always disproportionately targeted black people.
Sure. It makes sense, law should be protecting public health - it is a fair assumption. Now, there is a disagreement on the methods, whether making drugs more accessible would have a positive impact on the public health. A common basic argument just going per analogiam with alcohol doesn't have any sense in this context. It's a bit like a child's argument: "other children can binge youtube, why can't I, mommy?". Other arguments, like the lack of quality control in the illegal market, are different - they can't be reversed in such a childish manner and should be taken seriously.
PS Your point of view is very US-centric, I assure you the arguments against drugs in country I live might have been invalid, but definitely not racist.
I disagree that the alcohol comparison is not useful. I think many people in the US take lots of their social world as axiomatic and correct and natural. Two such "axioms" are the legality of alcohol and the illegality of "other drugs." The comparison with alcohol helps those who have not considered drug laws in good faith break out of their stupor and realize the "axioms" are created socially. The hope is that they will realize that the supposedly natural distinction between alcohol and other drugs is illusory.
Anyone who knows the history of the war on drugs knows that public health is a cover story. The first drug laws in the USA were bans on cocaine and heroin, and the arguments presented to Congress and the general public were overtly racist. It was said that cocaine turned black men into murderous demons who could not be stopped even after being shot in the heart. Heroin, besides being made by a German company, was also said to be popular among Asian immigrants who were bringing their awful habits here. Then marijuana was banned, because, according to the testimony given to Congress, it fueled jazz music and caused white women to want to have sex with black men, and Mexicans were using it to corrupt the white youth. Drug enforcement has always disproportionately targeted black people.