Disjointness can be expressed by two universal negative propositions:
No human is a horse.
No horse is a human.
If no instance of the first lies in the second, there is equally no instance of the second in the first. Disjointness is therefore symmetric.
A single statement such as “Zayd is not a horse” is not enough to prove the universal relation. The classification concerns all instances of both concepts, not one isolated example.