A person who has “two left left” is clumsy and can’t do various things, such as dance, play soccer, or march. The “two left feet” expression was popularized by the"Chiimie Fadden” Bowery boy dialect stories of Edward W. Townsend (1855-1942) that were published in the New York (NY) Sun in the 1890s. “You belong over by de odder truck, for you’ve got two left feet” was published in The Sun on October 28, 1894. ““Some Queer Boston Slang,” published in the Boston (MA) Daily Advertiser on November 16, 1894, explained:
 
“When you say a man has two left feet it is the same as intimating he is foolish, and it was that he desired to convey.”
 
“He’s a good boy, only he has two left feet, and I could learn Little Miss Fannie’s doll to dance easier nor him” was published in Townsend’s Chimmie Fadden and Mr. Paul (1902). “Besides, he tangoes like he had two left feet” was cited in a 1914 novel.
 
“Why can’t dogs (four-legged animals) dance?”/“Because they have two left feet”  and “Dressage horses dance really well for having two left feet” are “two left feet” animal jokes.
 
   
Wiktionary: two left feet
Noun
two left feet
1. (idiomatic) Clumsiness, especially at dancing or at soccer
He should stay off the dance floor with his two left feet.
 
(Oxford English Dictionary)
Phr. two left feet: signifying a clumsy person.
1915   P. G. Wodehouse Psmith, Journalist xviii. 132   Mr. Dawson..gave it as his opinion that one of the lady dancers had two left feet.
1959   E. L. Mascall Pi in High 7   Or dance with two left feet the valse triste.
1975   D. Ramsay Descent into Dark iii. 92   Clumsy..you’ve got two left feet.
   
Chronicling America
28 October 1894, The Sun (New York, NY), “Chimmie Fadden on the Stump” by Edward W. Townsend, pg. 4, col. 6:
“I knowed de mug, and I points nie finger at him and says: ‘Say, Plug Jacobs of O’Rafferty’s Roost, you don’t belong here; you belong over by de odder truck, for you’ve got two left feet.’”
 
Chronicling America
30 October 1894, The Sun (New York, NY), “Insect O’Connor Interprets,“pg. 1, col. 3:
“De feller says ‘G’wan, ye got two left feet.”
 
31 October 1894, Philadelphia (PA) Inquirer, “By an Ex-Editor,” pg. 6, col. 5:
Toward the President Hill has all along been using language like that of Mr. “Insect” O’Connor, one of the eminent statesmen of the New York city Congress district known as “de Ate,” saying to the great Grover, “Soy, yer got water in yer meter,” and “Yer trolley’s twisted,” and “G’wan, yer got two left feet,” and asking the CHief Executive to tie his face in a knot and threatening to sew a button on him and to “pull de ‘eart” out from under him.
 
16 November 1894, Boston (MA) Daily Advertiser, “Some Queer Boston Slang,” pg. 2, col. 4:
That was easily understood however and the examination went on swimmingly till he was told how they “jollied him for a good thing as if he had two left feet.” When you say a man has two left feet it is the same as intimating he is foolish, and it was that he desired to convey.
       
Google Books
“Chimmie Fadden” ; Major Max: And Other Stories
By Edward Waterman Townsend
New York, NY: Lovell, Coryell & Company
1895
Pg. 170:
“I knowed de mug, and I points nie finger at him and says: ‘Say, Plug Jacobs of O’Rafferty’s Roost, you don’t belong here; you belong over by de odder truck, for you’ve got two left feet.’”
 
Google Books
Mr. Dooley in Peace and in War
By Finley Peter Dunne
Boston, MA: Small, Maynard & Company
1898
Pg. 183:
To march well, a man’s feet have to be mates ; an’, if he has two left feet both runnin’ sideways, he ought to have interference boots to keep him fr’m settin’ fire to his knees.
   
Google Books
Chimmie Fadden and Mr. Paul
By Edward Waterman Townsend
New York, NY: The Century Company
1902
Pg. 175:
He’s a good boy, only he has two left feet, and I could learn Little Miss Fannie’s doll to dance easier nor him.
 
25 June 1902, The Upper Des Moines (Algona, IA), “Will Interest the Dancers,” pg. 9, col. 4:
It has been pointed out that a man seems to need two left feet to do this and that the chasse is a little complicated.
   
Google Books
What Will People Say?:
A Novel
By Rupert Hughes
New York, NY: Grosset & Dunlap
1914
Pg. 36:
“Besides, he tangoes like he had two left feet.”
   
OCLC WorldCat record
The Man with two Left Feet, and other stories
Author: P G Wodehouse
Publisher: London : Methuen & Co., 1917, 1922.
Edition/Format:   Book : English
 
Google Books
Fore!
By Charles Emmett Van Loan
New York, NY: George H. Doran Company
1918
Pg. 134:
He danced the one-step, of course — the only dance ever invented for men with two left feet — but his conception of the fox trot would have made angels weep, and I never realised how much hesitation could be crowded into a hesitation waltz until I saw BIll gyrate slowly and painfully down the floor.
   
OCLC WorldCat record
The curiosity of Mr. Treadgold
Author: Valentine Williams
Publisher: Boston : Houghton Mifflin Co. ; Cambridge : Riverside Press, 1937.
Edition/Format:   Book : Fiction : English
Contents:
The man with the two left feet—
 
OCLC WorldCat record
Two left feet : fox-trot
Author: Ralph Gordon
Publisher: New York City : J. Davis, ©1938.
Edition/Format:   Musical score : No Linguistic Content
Publication: WFAA collection.
 
OCLC WorldCat record
I’ve got two left feet : The New Grand Terrace Revue : 8th edition.
Author: Gerald Marks
Publisher: ©1940.
Edition/Format:   Musical score : English
 
OCLC WorldCat record
(Me and my) two left feet : from the film Two left feet.
Author: Philip Green
Publisher: ©1965.
Edition/Format:   Musical score : English