#1107: Sports Cheat Sheet explain

[A three-column table. Months are arrayed down the first column, the second and third columns show sports, with the divisions in partial months rather than lined up with the ends of months. American football and association football (i.e. soccer) are differentiated by small icons in brackets depicting the respective balls used.]

Which sport are they arguing about?

-My cheat sheet-

[The second column, reproduced using approximate dates.]

US:

Football [ovoid ball drawn in brackets]: January 1 - February 10

Basketball: February 10 - April 20

Baseball: April 20 - May 25

Basketball: May 25 - June 15

Baseball: June 15 - August 20

Football [ovoid]: August 20 - October 5

Baseball: October 5 - October 20

Football [ovoid]: October 20 - December 31

[The third column, reproduced using approximate dates.]

non-US:

Football [truncated icosahedron, 20 hexagons and 12 pentagons]: January 1 - December 31