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Last time I took the high speed train they left us a reminder on the ticket about how much less carbon the travel was with them. I wondered then, why was it still cheaper to fly? I took the train that time for convenience as it was direct but not much cheaper.

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Infrastructure. A train isn't just a vehicle but thousands of miles of track that must be maintained. The higher the speed, the greater the cost to build and maintain that track. Airplanes need runways, but those are a pittance to maintain compared to rail lines. Land is also 2d finite resource that must be dedicated to rail travel. Airspace is 3d.

There's much less competition (if any) in rail travel for any given route.

Definitely not the case in EU and where so, it's only because of governmental inference in the market. Czechia deregulated few years ago and instantly (literally the first day the deregulation came into effect) there was 10+ new rail travel companies operating on basically every conceivable route.

There's also no tax on jet fuel.

A high speed train almost always has a lower speed competitor, although it may be run by the same company.

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