Sure it is! Have you ridden it? It is underground, in a tunnel that's perhaps 5 miles long, has a system of 5 lines which branch off at either end, and the trains themselves are composed of multiple cars linked together as the trains travel down the tube. It's not until you leave the underground system at either end that the subway train separates into different lines and it becomes the streetcar, which may still be composed of a number of cars linked together as a train. If this doesn't qualify as a "subway", I'm not sure what your definition is.

I wonder if you're confusing it with the "F-Market" line, which is composed of historic streetcars that travel on the surface down Market St., and then go up the Embarcadero to Fisherman's Wharf, or the Cable Cars? THEY aren't subways, for sure. But the Muni Metro Subway even labels itself as one.

Many visitors don't know about it or use it; those of us who live here and work in downtown use it a lot. As a note, they are currently building another line, which will go down the Third St. corridor from near Candlestick Park up across Market St to Chinatown. The line from Pacbell Park to Chinatown is again supposed to be a subway. This is one of Willie Brown's legacies.