Because it says so in the Constitution - "The Congress shall have the power to establish Post Offices and post Roads". The Congress has delegated that power to the states (except for the Interstates), and every state says that every road that has a mailbox on it is a post road, so there you go.
If we can solve your problem and provide more travel options with privately-built and funded, for-profit mass transit, I'm all for that. Charge whatever you want, don't block or interfere in any way with any post road, and have at it. But gov't built and ran public transportation is theft from a majority of taxpayers to serve a minority of them, and is evil.
I'm going to re-write your argument in technical format:
Premise 1: The constitution provide power to the government
Premise 2: The power is to establish post offices and post roads
Premise (unstated) 3: The government has no other powers to establish transit systems
Premise 4: Tax money is collected
Premise 5: Tax money is used for mass transit systems
Premise (unstated) 6: tax money used for any other purpose than defined by the constitution is unlawful
Conclusion: It is illegal for the government to use tax money for mass transit systems.
So, this is a logical argument. This means that all the premises do support the conclusion. Some were unstated, so I had to extrapolate them, but I feel relatively confident I captured your argument. The issue is just because an argument is logical, does not make it a true argument. To test if the argument is true, we must test if the premises are true. We can all agree that a number of these premises are true. For instance 1, 2, 4, & 5 all appear to be true. However, I'm not sure I would agree that #3 or 6 are true. For instance, in #3, governments establish transportation systems all the time. One would assume if this were an illegitimate use of tax payer funds, there would be fairly decisive decisions from the courts prohibiting it. In addition on item #6, various levels of government use funds on items other than that dictated by the constitution relatively frequently. Again, I would have expected a decision from the courts prohibiting it.