“Everybody makes mistakes—that’s why they put erasers on pencils” (or “that’s why pencils have erasers”) is a saying that dates to at least 1915. The saying is used in government, schools, science, business, sports and other fields—wherever people make mistakes.
       
 
Wikipedia: Pencil
Eraser attached
On 30 March 1858, Hymen Lipman received the first patent for attaching an eraser to the end of a pencil. In 1862 Lipman sold his patent to Joseph Reckendorfer for $100,000, who went to sue the pencil manufacturer Faber-Castell for infringement.  In 1875, the Supreme Court of the United States ruled against Reckendorfer declaring the patent invalid.
     
Google Books
February 1915, The American Printer, pg. 728, col. 2:
The Free Press Printing Company, Burlington, Vt.—The Christmas folder is appropriate and pleasing. The blotters are also interesting, especially the one containing this phrase: “Every one makes mistakes — otherwise it would not pay to put erasers on pencils.”
     
Google Books
September 1917, The Postal Record, pg. 222, col. 1:
We may be mistaken — everybody makes mistakes; that is why the eraser is on the end of the pencil.
 
15 August 1919, Fort Des Moines (IA) Post, pg. 5, col. 4:
Everyone makes mistakes—that’s why there are erasers on pencils.
 
Chronicling America
10 September 1919, Edgefield (SC) Advertiser, pg. 7, col. 3 ad:
Everybody makes mistakes. That’s why they put erasers on lead pencils.
(The Bank of Trenton, S. C.—ed.)
   
Google Books
Personal Leadership in Industry
By David Rankin Craig and Werrett Wallace Charters
New York, NY: McGraw-Hill
1941    
Pg. 42:
“Everybody makes a mistake now and then. That’s why they put erasers on pencils.”
 
Google News Archive
12 November 1952, Ottawa (Ontario) Citizen, “Writer’s Desk Draped Black,” pg. 25, col. 2:
Last year, when Bombers were whipped in the semi-final, Coach George Trafton said the team had made plenty of errors “but that’s why they put erasers on pencils.”
 
Google Books
“Miss Library Lady”
By Ann McLelland Pfaender
New York, NY: J. Messner
1954
Pg. 105:
That’s why pencils have erasers and automobiles have bumpers!
   
Google Books
Fräulein
By James McGovern
New York, NY: Crown Publishers
1956
Pg. 264:
“Everybody makes mistakes,” he observed. “That’s why they’ve got erasers on pencils.”
 
Google News Archive
5 November 1964, Spokane (WA) Daily Chronicle, “Buggies Were Big” by Hal Boyle, pg. 4, col. 3:
You could win a reputation as a wit by saying things like, “Everybody makes mistakes —that’s why they put erasers on pencils.”