“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 is from 1943, “fanatic—One who can’t change his opinion and won’t change the subject.”
 
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.”
 
[This entry was prepared with research assistance from the Quote Investigator.]
     
 
Esar’s Comic Dictionary
By Evan Esar
New York, NY: Harvest House
1943
Pg. 101:
fanatic.
A person who redoubles his efforts after having forgotten his aims.
One who can’t change his opinion and won’t change the subject.
 
23 May 1945, Oakland (CA) Tribune,  “Dizzy Daffynitions” by Paul H. Gilbert, pg. 8, col. 5:
FANATIC: One who can’t change his opinion and won’t change the subject.
   
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.
 
Irrepressible Churchill:
A Treasury of Winston Churchill’s Wit
By Kay Halle
Cleveland, OH: World Publishing Company
1966
Pg. 308:
EAR-WITNESS
W.S.C.: A fanatic is one who can’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.’”