According to R. Ken Rasmussen in The Quotable Mark Twain (1998), this is most probably not Twain's.
Misattributed
Mark Twain: Zitate auf Englisch (seite 2)
Mark Twain war US-amerikanischer Schriftsteller. Zitate auf Englisch.
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“The two most important days in your life are the day you were born and the day you find out why.”
This appears on the opening placard of the film The Equalizer, attributing it to Twain, but there is no evidence that Twain wrote it. A precursor is found in Taylor Hartman's self-help book The Character Code (first published 1991), where it is not attributed to Twain: "The three most significant days in your life are: 1. The day you were born. 2. The day you find out why you were born. 3. The day you discover how to contribute the gift you were born to give" ( Google Books link https://books.google.com/books?id=gIKCxWxNmeMC&pg=PA147&dq=%22day+you+find+out+why%22&hl=en&sa=X&ved=0ahUKEwijrJzc84vLAhUJzGMKHajvADEQ6AEIIjAB#v=onepage&q=%22day%20you%20find%20out%20why%22&f=false)
Disputed
“It is better to keep your mouth shut and appear stupid than to open it and remove all doubt.”
Cited as an example of "What Mark Twain Didn't Say" in Mark Twain by Geoffrey C. Ward, et al.
Misattributed
Variante: It is better to keep your mouth closed and let people think you are a fool than to open it and remove all doubt.
Attributed to Twain but never sourced, this quotation should not be regarded as authentic.
Misattributed
Vol. II, p. 7
Mark Twain's Autobiography (1924)
“"Classic." A book which people praise and don't read.”
Mark Twain
buch
Following the Equator
Pudd'nhead Wilson's New Calendar, Ch. XXV
Following the Equator (1897)
Not by Twain, but from Edward Abbey's A Voice Crying In The Wilderness (1989).
Misattributed
Not found in Twain's works, this was attributed to him in Reader's Digest (September 1939): no prior attribution known. Mark Twain’s father died when Twain was eleven years old.
Disputed
Variante: When I was a boy of fourteen, my father was so ignorant I could hardly stand to have the old man around. But when I got to be twenty-one, I was astonished at how much the old man had learned in seven years.
“It's not the size of the dog in the fight; it's the size of the fight in the dog.”
Anonymous American proverb; since 1998 this has often been attributed to Mark Twain on the internet, but no contemporary evidence of him ever using it has been located.
Variants:
It is not the size of the dog in the fight that counts, but the fight in the dog that matters.
"Stub Ends of Thoughts" by Arthur G. Lewis, a collection of sayings, in Book of the Royal Blue Vol. 14, No. 7 (April 1911), cited as the earliest known occurrence in The Dictionary of Modern Proverbs, edited by Charles Clay Doyle, Wolfgang Mieder, and Fred R. Shapiro, p. 232
It is not the size of the dog in the fight that counts, but the fight in the dog that wins.
Anonymous quote in the evening edition of the East Oregonian (20 April 1911)
What counts is not necessarily the size of the dog in the fight — it's the size of the fight in the dog.
Dwight D. Eisenhower, declaring his particular variant on the proverbial assertion in Remarks at Republican National Committee Breakfast (31 January 1958) http://www.presidency.ucsb.edu/ws/index.php?pid=11229
Misattributed