The quality or state of being abusive; the character of treating others with cruelty.
From abusive + -ness (suffix creating abstract nouns from adjectives), the modern standard formation for discussing the abstract quality of being abusive.
Words ending in '-ness' are incredibly productive in English because they follow a predictable pattern—you can add '-ness' to almost any adjective and English speakers will understand it immediately, even if the specific word is new.
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