“You can’t push yourself forward by patting yourself on the back” is a motivational saying that has been cited in print since at least 1921. Authorship is unknown.
 
“You cannot propel yourself forward by patting yourself on the back” is a slightly different version that has been cited in print since at least 1992.
 
     
Google Books
The Gregg Shorthand Magazine
Volume 4
1916 (This Google Books date is possibly incorrect.—ed.)
Pg. 185:
It’s not the least little bit of use trying to push yourself forward by patting yourself on the back. It can’t be done.
 
17 August 1921, Ironwood (MI) Daily Globe, “Your Views and Mine” by Shakes, pg. 4, col. 2:
COMES THIS CARD IN THE MAILS: “You can’t push yourself forward by patting yourself on the back.”
 
Google News Archive
5 April 1943, Spartanburg (SC) Herald, Walter Winchell syndicated column, pg. 4, col. 3:
Advertiser’s Digest: You can’t push yourself forward by patting yourself on the back.
   
Google News Archive
15 February 1984, The Hour (Norwalk, CT), pg. 5, col. 2:
Thought for today: “You can’t push yourself forward by patting yourself on the back.” —Anonymous.
   
Google Groups: rec.arts.disney
Theme Park Update(s)
Jim Schnell
1/27/92
(...)
You cannot propel yourself forward by patting yourself on the back.
 
Google Books
20,000 Quips & Quotes
By Evan Esar
New York, NY: Barnes & Noble Books
1995, ©1968
Pg. 652:
You can’t push yourself forward by patting yourself on the back.
 
Google Books
552 Questions That Make You Go “Hmmmmm!” / 87 Great Put Downs!
By Wayne Cundal
Bloomington, IN: AuthorHouse
2010
Pg. 30:
267. Did you know you can’t propel yourself forward by patting yourself on the back?
 
Twitter
McDonald’s Lover
‏@yesiluvmcds
You cannot propel yourself forward by patting yourself on the back.
2:59 PM - 24 Apr 2015