quarrel vs polemicize

quarrel is a noun but polemicize is not a noun.

Word	Noun	Adjective	Verb	Adverb
quarrel	Yes	No	Yes	No
polemicize	No	No	Yes	No

As verbs, polemicize is a hyponym of quarrel; that is, polemicize is a word with a more specific, narrower meaning than quarrel:

Other hyponyms of quarrel include brawl, wrangle, spat, polemicise, polemise, polemize, fall out.

quarrel (noun)	polemicize (noun)
an arrow that is shot from a crossbow; has a head with four edges
an angry dispute

quarrel (verb)	polemicize (verb)
have a disagreement over something	engage in a controversy