"A fanatic is one who won’t change his mind and won’t change the subject” is a well-known saying that’s often attributed to Winston Churchill (1874-1965), but Churchill scholars haven’t found a verified citation. The first known citation—from December 1949—includes “can’t change his opinion” rather that “won’t change his opinion”:

“Fanatic: One who can’t change his opinion and won’t change the subject.—Everson News.“

Winston Churchill was credited—correctly or incorrectly—by May 1952: “‘A fanatic,’ says Winston Churchill,’"is one who can’t change his mind and won’t change the subject.’” By at least November 1952, “radical” replaced “fanatic” and “won’t change his mind” replaced “can’t change his mind.”


13 December 1949, Seattle (WA) Daily News, pg. 6, col. 2: 
Fanatic: One who can’t change his opinion and won’t change the subject.—Everson News.

Google News Archive
28 May 1952, Rock Hill (SC) Evening Herald, pg. 2, col. 1:
...By Any Other Name
“A fanatic,” says Winston Churchill, “is one who can’t change his mind and won’t change the subject.”
We thought that was a politician.

28 September 1952, Seattle (WA) Daily Times, “Daffynitions” by Paul H. Gilbert, pg. 13, col. 1:
FANATIC: One who can’t change his opinion and won’t change the subject.

13 November 1952, Mexico (MO) Evening Ledger, pg. 12. col. 5:
We recently heard a radical designated as “a person who won’t change his mind or won’t change the subject.”

Google News Archive
12 September 1963, Sherbrooke (Quebec) Telegram-Observer, “Editor’s Notebook,” pg. 6, col. 1:
A fanatic is one who won’t change his mind and won’t change the subject.

Google News Archive
27 November 1968, Reading (PA) Eagle, pg. 10, col. 4:
Purloined Chuckle: “A fanatic is a man who won’t change his mind and won’t change the subject.” Johnstown Tribune-Democrat.

Richard M. Langworth (Churchill historian, automotive and travel writer)
Definition of “Fanatic”
18 March 2009
Can you ver­ify whether or not Churchill said: “A fanatic is some­one who won’t change his mind and won’t change the sub­ject”?  —T.M., Ontario, Canada

Sorry, it’s not Churchill. From Churchill by Him­self, the “Red Her­rings” appen­dix (unat­trib­uted quotes), page 574: “Often attrib­uted to Churchill or Pres­i­dent Tru­man. Ralph Keyes, edi­tor, The Quote Ver­i­fier, writes: ‘It’s a quo­ta­tion I see often, but with­out a source. I doubt that it’s Tru­man, or, if he ever said it, that the quo­ta­tion orig­i­nated with him.’”