Carr was born Joseph Francis Karr on October 23, 1879, at his parents' home in the Irish neighborhood on the East End of Columbus, Ohio. His father, Michael Karr, was a shoemaker who was born in Ireland in 1841 and immigrated to the United States in 1864. His mother Margaret Karr was born in New York to Irish immigrant parents. Carr had five older siblings, Bridget, James, John, Mary, and Michael, and a younger brother, Edward.

In the early 20th century, college football was the dominant version of the sport, and professional teams would sometimes pay college players to play for them, often under assumed names. The practice was considered questionable ethically, resulting in taint being associated with the professional game. In order to remove the taint, and to engender peaceful relations with the college game, Carr made it one of his first goals as league president to impose a strict ban the use of college football players. Indeed, at the same meeting at which Carr was elected president, the APFA adopted a rule prohibiting teams from using players who had not completed their college course.  Carr enforced the ban with vigor. During the 1921 APFA season, two or three college players from Notre Dame played for the Green Bay Acme Packers under assumed names. The incident resulted in the players losing their amateur status and being barred from further college football participation. In January 1922, Carr responded with the severest possible action, kicking the Packers out of the APFA. A few months later, a group headed by future Hall of Famer Curly Lambeau applied for and was granted the Green Bay franchise.  The 1925 Chicago Cardinals-Milwaukee Badgers scandal followed four years later. In December 1925, four high school students played for the Milwaukee Badgers in a game against the Chicago Cardinals. Carr responded by imposing stiff penalties. The Milwaukee club was fined $500 and given 90 days within which to "dispose of all its club assets at which time the management must retire from the league." The Cardinals were fined $1,000 for their prior knowledge of the violation, and Cardinal player Art Foltz was temporary banned from the league for live for having "induced the boys to play".  The issue arose again when Red Grange, star halfback of the University of Illinois football team, signed with the Chicago Bears. Grange played his final college game on November 21, signed with the Bears the next day, and appeared in his first professional game on November 26. Two weeks later, Ernie Nevers signed a professional football contract for $50,000. To help ease tensions and promote the professional game in the college circles, Carr established a rule prohibiting college players to sign with professional teams until after their class had graduated. These decisions gave the NFL credibility and much needed support from the colleges and universities from across the country.

Who initiated the ban?
the APFA adopted a rule prohibiting teams from using players who had not completed their college course.