Why is travel by train more expensive than travel by airline?

I am assuming you are referring to the U.S. rail system.

It is the logistics of operating a rail line that cause the overhead to be quite high, thus translating to high ticket the prices.

Aside from the normal costs such as administrative and staff compensation, there is the cost of maintaining the rails themselves along with the stations. (I'm not sure if that is the responsibility is borne by the state whereupon the rail company is billed in terms of a recurring fee.)

Other costs would be operating a restaurant/bar as you mentioned and the number of people they can transport per unit time. Plus the cost of fuel for they still operate using diesel engines.

The airlines can transport thousands of people per day. Plus the airlines have either modified their existing aircraft (ex. inflected wing) or purchased new models (Boeing 787) which vastly improved their fuel efficiency.

However, there are ways the rail systems can save money such as employing engines that are hybrid electric. (CSX uses hybrid electric technology which improves efficiency by 30%)

I do too enjoy traveling by rail when I had to for previous employment.

I have no idea - but it's frustrating when looking to travel in a more green manner that the cost is pretty prohibitive doing so long-distance / internationally

You must of been looking at some very weird train fares if you think that.