'non-aggressive' is formed in English from the prefix 'non-' (a negating element meaning 'not') plus 'aggressive.' 'Aggressive' ultimately comes from Latin via French: from Latin 'aggredi/aggrescere' (elements 'ad-' + 'gredi/gressus' meaning 'to step, go toward') with the sense of 'attack' evolving in later usage.

'aggressive' entered English via French (Old French/Modern French 'agressif'/'aggressif') and Late Latin forms such as 'aggressivus' (from the past participle stem 'aggress-'). The negative prefix 'non-' is a straightforward English/Latin-derived negator; combining gives 'non-aggressive' and the adverbial form 'non-aggressively'.

Originally related to 'to step toward' or 'to attack' (Latin root), 'aggressive' developed the sense of 'hostile or attacking behavior'; 'non-aggressive' and 'non-aggressively' thus mean 'not hostile/attacking' or 'without aggression' in modern usage.