Why are you "On a train" yet "In a car" when you are inside both vehicles?
"On a bike" makes sense but "On a plane" seems wrong as you are actually inside the plane rather than on it.
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Generally speaking, the metaphoric senses of get on and get in follow dimensionality:
In terms of conveyances,
This much is predictable.
The problem arises with scheduled public conveyances;
in that case only,
a human who gets in the conveyance physically
also is on the roster of passengers metaphorically
(on the roster is a 2-D "page/paper" metaphor).
So one can be said to get on the bus, the plane, the train, the trolley; but not the taxi.
I remember different opinions on that:
When you get in the car, you get directly into your seat, while on public transport you have to walk to it (plane, train, bus).
You can stand up and walk around in public transport, thus the "on".
Public transport is "elevated", you need to go up a bit to get on it (stairs, platform).
"car" deriving from "carriage", a vehicle mounted with a car. That also explains why we get on the train, but in the train car.