To reduce someone's courage, confidence, or will to resist; to cause someone to lose hope or faith in something.
From French demoraliser, formed from de- (down/away) + morale (moral courage/spirits). The French term was coined in the late 18th century and adopted into English, particularly British English which retains the -ise spelling.
To demoralise is to attack the spirit rather than the body—it's why propaganda, censorship, and crushing defeats in war matter so much. An army can lose without being physically destroyed if its morale collapses first!
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