I used to think this, but it's not technically true.
Passenger trains reliably made money on fare revenue alone during the early years, 1828 through 1895 or so.
It became impossible for passenger trains to make money on fare revenue alone when two things happened:
(1) Motorcars were introduced
(2) Paved roads were subsidized heavily by all levels of government, starting in the 1890s and becoming a huge flood of funding in the 1920s. It got much more extreme in the 1950s.
Competing with horse-drawn carriages was easy. Passenger trains made lots of money.
Even with motorcars being sold by Ford and others, passenger trains made money as long as the motorcars had to drive on pitted dirt roads across the country.
Once the taxpayers started subsidizing lavishly paved rural highways, *that* is when it became impossible for passenger trains to make money on fare revenues alone.
This gives some perspective. Anthony's description is accurate for the post-1920 situation for passenger trains.
So my position has always been: give the passenger trains the same amount of government funding we give the roads. One calculation from 2007 said that $146 billion was spent by federal, state, and local government on roads THAT YEAR. So I'm comfortable with $146 billion in funding per year. Currently passenger trains of all sorts get much less than that.