hate (v.)
Old English hatian "to hate," from Proto-Germanic *haton (cognates: Old Saxon haton, Old Norse hata, German hassen, Gothic hatan "to hate"), from PIE root *kad- "sorrow, hatred" (cognates: Avestan sadra- "grief, sorrow, calamity," Greek kedos "care, trouble, sorrow," Welsh cas "pain, anger"). Related: Hated; hating. French haine (n.), hair (v.) are Germanic. Hate crime attested from 1988.
hate (n.)
Old English hete "hatred, spite," from Proto-Germanic *hatis- (cognates: Old Norse hattr, Old Frisian hat, Dutch haat, Old High German has, German Hass, Gothic hatis; see hate (v.)). Altered in Middle English to conform with the verb. Hate mail is first attested 1967.