Given the dearth of private subway companies, I question this claim. There are lots of places where a subway would be highly desirable but doesn't exist, why hasn't some entrepreneurial soul built one already?
The London Underground, the earliest subway system, was initially built as a patchwork of private railway systems that were later brought under government control.
Most of the subsequent systems (e.g. Paris, Moscow, St. Petersburg) used the London system as a reference.
So, mass transit did in fact arise as a result of private entrepreneurship. The reason subways don't exist in places where it would be 'desirable' is because of government interference, or simply poor economics.
And I'm not even a libertarian.
http://www.historytoday.com/richard-cavendish/first-day-lond...
http://en.wikipedia.org/wiki/Metropolitan_Railway#Establishm...
Same deal with new York's subway - therre were private companies involved but they were set up within the frameworks of a public works project and were basically financial vehicles designed to limit financial liability and attract some matching capital from the private sector for an initial large public sector investment or monopoly grant.
I'm sympathetic to libertarianism but this notion that all this stuff would happen by itself if it weren't for evil government interference is just bollocks, it's just as stupid as communists claiming that all private capital is wicked.