"The boy stated that, while he loved football, he didn't play it every day."
"while he loved football" is a clause inserted into another clause ("that he didn't play it every day"). We keep the two ideas separate by marking the interposed clause off with commas.
compare:
"The boy stated that he loved football, but he wouldn't expect his son to play it."
Here, the 'but' clause is an independent clause (subject + verb + it makes sense by itself and therefore expresses a complete thought), and is marked off with a comma preceding it.
compare:
"The boy stated that he loved football but didn't play it every day."
The 'but' clause does not have a subject, so is not an independent clause.