polemic vs arguing

polemic and arguing both are nouns.

Word	Noun	Adjective	Verb	Adverb
polemic	Yes	Yes	No	No
arguing	Yes	No	No	No

As nouns, arguing is a hypernym of polemic; that is, arguing is a word with a broader meaning than polemic:

polemic: a controversy (especially over a belief or dogma)
arguing: a contentious speech act; a dispute where there is strong disagreement

Other hypernyms of polemic include argument, contention, contestation, controversy, disceptation, disputation, tilt.

polemic (noun)	arguing (noun)
a controversy (especially over a belief or dogma)	a contentious speech act; a dispute where there is strong disagreement
a writer who argues in opposition to others (especially in theology)

polemic (adjective)	arguing (adjective)
of or involving dispute or controversy