Why should I, a taxpayer, subsidize rails?

It's sarcasm, many drivers don't realize that the public subsidizes them too, but have such silly arguments.

No, it's actually a good question. If the rails are private, why should the public subsidize them?

For clarity's sake, I think railways should be public, and paid for with a combination of taxes and fares.

I think rails should be public, like skies and roads, and train companies should pay for their usage.

That sounds like an excellent idea. However I think rail transport depends more heavily on quality infrastructure. If a state doesn’t maintain its roads well and allow potholes to develop, it is probably rare for that to cause a fatal accident (I’ve heard of potholes causing damage to cars but not deaths). But improperly maintained rails lead to derailments and deaths.

Potholes do regularly result in cyclists' deaths.

You may still need a public train service or subsidies of some kind to make sure unprofitable but vital routes get served

That's how it was in wild west US as well. The rail lines got massive land grants.

https://en.wikipedia.org/wiki/Pacific_Railway_Act_of_1862

This is one of the ways the US funded rail infrastructure in the 1800s.

So they're basically a real estate company with a rail transport component?