Basically, quarks seem to have charges that are 1/3 e. However, they can only be stable in groups of three, and those groups must have an integer value. So the only possibilities are -1, 0, and 1.
As to why the above is true, it just seems to be a rule. We don't have any good reasoning for why that rule exists.
And, more specifically:
https://en.wikipedia.org/wiki/Elementary_charge#Charges_less...
Basically, quarks seem to have charges that are 1/3 e. However, they can only be stable in groups of three, and those groups must have an integer value. So the only possibilities are -1, 0, and 1.
As to why the above is true, it just seems to be a rule. We don't have any good reasoning for why that rule exists.