It is much easier to travel with pets on trains.
The prices of the tickets are cheaper and does not change as much as airfare.
There is much more leg space and traveling is much more comfortable.
There is no limit on luggage, you can carry as many bags as needed.
You don't have to keep sitting on the seat and safety belts are not required.
You get to see the scenic route and breathe in fresh air.
It is easier to reach the center of many cities.