“Cast not a stone at every dog that barks” is a proverb that has been cited since at least 1579. British statesman Winston Churchill (1874-1965) said in 1923:
 
“You will never get to the end of the journey if you stop to shy a stone at every dog that barks.”
 
Churchill’s statement—actually just a restatement of an old saying— is often cited as a business proverb, meaning that you can’t fight and win every battle. To succeed in business or in life, once should fight only the important battles.
 
 
UsingEnglish.com
Idiom Definitions for ‘Don’t stop and kick at every dog that barks at you’
If we stop to kick at every dog that barks at us we will never arrive at our destination in life, because we are obsessed with righting insignifigant wrongs that should have no more effect on us then a dog that barks as we walk by.
 
Google Books
Orpheus and Eurydice: With the Pantomime Entertainment
By Henry Sommer
London: Printed for C. Corbett
1740
Pg. iii:
Altho’ it is a common Saying, that one ought not to throw a Stone at every Dog that barks at him; yet when a little Dunghill Curr barks and bites too, it would be an unpardonable Indolence not to give him some Chastisement.
 
Google Books
A Narrative of Three Years’ Residence in France
Volume 3
By Anne Plumptre
London” Printed for J. Mawman, et al.
1810
Pg. 196:
Ne quet red taoler mein och quement ki a ar.— You should not throw a stone at every dog that barks.
 
4 October 1903, Winston-Salem (NC) Journal, “Kickers Kolum,” pg. 2, col. 1:
“I will say I do not often stop to throw bricks at every dog that barks at me, nor either do I have customers waiting until 9 p. m. for goods purchased during the day.
(...)
S. O. Bennett
 
Google Books
Sermons
By George Rutledge Stuart
Philadelphia, PA: Pepper Publishing Company
1904
Pg. 129:
He who kicks at every dog that barks at him will have a sprained knee, his breeches torn, or wear dob-slobbers half the time. He who fights at the barking dog is very little bigger than the dog that barks.
 
28 April 1908, Cleveland (OH) Plain Dealer, “Cleveland Men Demand Search,” pg. 11, col. 3:
“I have not answered many personal flings because I do not stop to throw stones ar every dog that barks,” retorted Howe, “but I want to say that I alone am responsible for the amendments as proposed and no one else.”
     
Google Books
A Coach’s Life:
My Forty Years in College Basketball
By Dean Smith with John Kilgo and Sally Jenkins
New York, NY: Random House
2000
Pg. ?:
Or, “Dean, you can’t stop at every dog that barks or you’ll never get the mail delivered.”
 
Google Books
Churchill by Himself:
The Definitive Collection of Quotations
By Richard Langworth
London: Ebury Press
2008
Pg. 579:
Shy a stone
You will never get to the end of the journey if you stop to shy a stone at every dog that barks.
1923, 3 DECEMBER. SHEPHERD’S BUSH EMPIRE, LONDON. (CS IV, 3426.)
WSC was quoting someone else. He preceded this by stating, “As someone said…” A similar statement urging courage “when the dog growls” is in Chapter 29, Leadership…COurage.
     
Google Books
Future Brain:
The 12 Keys to Create Your High-Performance Brain
By Jenny Brockis
Milton, Qd: John Wiley & Sons Australia, Ltd
2016
Pg. 73:
As Sir Winston said, ‘You will never reach your destination if you stop and throw stones at every dog that barks’.
 
We need to be able not only to focus, but to fix that focus and narrow it to an attention span that remains constant and unwavering.
 
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“You will never reach your destination if you stop and throw stones at every dog that barks.” - Winston Churchill
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5:55 PM - 18 Jan 2016