Because "fan" is a pasteurized abbreviated term for its root word: "fanatic".
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According to Merriam-Webster, a fanatic is a person who is excessively enthusiastic or devoted to a cause, interest, or activity. The term can be used to describe someone who is extremely devoted to a controversial matter, such as religion or politics, or someone who is very enthusiastic about a sport or activity.
The word fanatic comes from the Latin word fanaticus, which means "of a temple" and "enthusiastic, inspired". The word's original meaning was "frantic, frenzied, mad", which came from the idea that people who behaved in this way were possessed by a deity. This meaning is now obsolete.
Synonyms of fanatic include:
extremist, activist, militant, zealot, bigot, and hothead.