Why is the chemical symbol for zinc Zn?

There does not seem to be any rational reason, other than general agreement.

The symbols for elements generally used single letters for the earliest discoveries, espeically when there were fewer elements with similar names. The name "zincum" was likely from one of several German words (zinn= tin, zinke=toothed). The symbol Zn was in use long before the element zirconium was discovered.