Why is the zeroth law of thermodynamics even a law?

The zeroth law of thermodynamics states that if two thermodynamic
systems are each in thermal equilibrium with a third, then they are in
thermal equilibrium with each other. Accordingly, thermal equilibrium
between systems is a transitive relation.



The fact that temperature obeys a transitive property is by no means intuitive!

If A likes B; B likes C; Does not imply that A likes C.

The city closest to city A is B, the city closest to B is C, but A is not always the closest to C


Or this popular example.

Rock > Scissors, Scissors > Paper. But Rock > Paper is definitely not true