Syllable division derived from spelling — this word is not in the pronouncing dictionary, so no phonetic transcription is shown rather than a guessed one.
self-asserting is an adjective meaning "aggressively self-assured". It carries one recorded sense.
aggressively self-assured
“an energetic assertive boy who was always ready to argue”
“pointing directly at a listener is an assertive act”
Definitions, synonyms and semantic relations for self-asserting come from Princeton University’s WordNet. Commonness is measured against a corpus of everyday English. Full sources and licences.