Here's why you shouldn't. Yes, it's true that some goth kids or punk kids drink alcohol and do drugs. I didn't do either when I was in high school, but the vast majority of my peers did- the punk kids, the jock kids, the preppie kids, the goth kids and the girls in the National Honor Society. As far as I could tell, drug and alcohol use was so widespread in my high school it was almost as if I was the only one not doing it. So yes, these things are problems- but they're not defined by nor even really associated with an interest in a particular subculture.
So what is associated with interest in a subculture? A love of music for its own sake, rather than for perceived “coolness” or status issues. A desire for real community with shared culture, something that is drastically lacking in much of modern life. An interest in aesthetics, for the creation of beauty- though possibly of a type you wouldn't personally appreciate. A willingness to buck the mainstream, and the strength of character to do so.
Involvement in a subculture doesn't mean your kid is a messed-up deviant. It means your kid is growing up to be an interesting human being. (Of course, plenty of kids who aren't punks or goths are interesting human beings too!) You shouldn't fear your kid's involvement in a subculture. You should embrace it, and learn more about it. You might find out the stuff your kid is getting into is actually pretty cool.