Granted, Polish phonology differs from that of the other Slavic languages in several ways, but these two facts remain: Polish is a completely Slavic language by any standard, and Cyrillic, unlike the Latin alphabet, was made especially to fit Cyrillic phonology, and therefore is perfectly suited for it.

Why does Polish not use the Cyrillic alphabet?

Because Cyrillic alphabet was adopted with the Orthodox christianity in Kievan Rus. Poland was baptized by the western Katholic Church which was using Latin and Lathin alphabet.

What alphabet does Polish use?

The Polish alphabet also abecadło is the script of the Polish language, the basis for the Polish system of orthography. It is based on the Latin alphabet but includes certain letters with diacritics: the kreska or acute accent (ć, ń, ó, ś, ź); the overdot or kropka (ż); the tail or ogonek (ą, ę); and the stroke (ł).