Point 1 is not all that disputable nor is it an assumption. The scientific studies on the matter tend to support alcohol being one of the worse drugs we know about, in terms of harm to the individual, addiction potential and harm to society. It is exceeded by heroin, cocaine and tobacco, but little else (maybe meth I guess).

Point 2 is not an interpretation - it's again a fact, most people (over half) in western societies like the US and UK drink alcohol, a proportion which rises if we just look at the adult population. I'm not making the argument that alcohol should be legal, I'm saying that most people already think that. I agree here, if you want to be pedantic, that their consumption does not prove that, only implies it, but there is also likely a proportion of non-drinkers who think it should be legal. So again - I'm not making any claims about whether alcohol should be legal, I am making claims about the likely views of your interlocutor in a debate about legalisation.

Point 3 is simply stating that given point 1 is true (which it is, empirically, to the best of our current knowledge) and you are talking to someone in group 2 (which you probably are), then if they want to be self-consistent they ought to examine any negative views on legalisation.

This is an explanation of why an argument along the lines of "booze is legal" is often made and may be effective. NOT an attempt at a formal proof for why any particular drugs should be legal in isolation or a justification of alcohol's status. As such I'm afraid I find your response overly nit-picky.

A perfectly valid response to the argument is "But I don't necessarily agree that alcohol should be legal", which then widens the terms of the debate.