The right place for Football is
Team B.
Because
All of the words in both team a and team b are compound words (as well as football), but all of the words in team A, when the two words that make up the compound word are reversed, they make up another compound word.
Examples:
Butthead --> Headbutt/Birdsong--> songbird
And for set B:
Birdseed cannot become seedbird. Similarly, the others, like workload cannot be reversed as well.
So,
Football is in team B because there is no such thing as a 'ballfoot.'
Edit Dec. 2022:
Apparantly 'seedbird' is a word according to Merriam-Webster... Seedbird Definition Who would've thought? :)