Old English hatian "regard with extreme ill-will, have a passionate aversion to, treat as an enemy," from Proto-Germanic *haton (source also of Old Saxon haton, Old Norse hata, German hassen, Gothic hatan "to hate"), from PIE root *kad- "sorrow, hatred" (source also of Avestan sadra- "grief, sorrow, calamity;" Greek kēdos "care, trouble, sorrow, mourning, funeral rites;" Welsh cas "pain, anger"). Related: Hated; hating. French haine (n.), haïr (v.) are from Germanic.
Old English hete "hatred, spite, envy, malice, hostility," from Proto-Germanic *hatis- (source also of 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 1951. Hate crime is attested by 1988. Hate speech in modern use is attested by 1990. The term is found in a translation, published in 1898, of the Anglo-Saxon poem called "The Fall of the Angels," telling of Satan's revolt, where it renders Anglo-Saxon hetespraece:
Dear was he to our Lord; but it could not be hidden
That his angel began to be proud,
Lifted himself against his Leader, sought hate-speech,
Words of boasting against him, and would not serve God.
["Education," vol. xviii, No. 6, Feb. 1898]