Because the NFL IS a not for profit organization.
The TEAMS however are for profit.
You misunderstand the dynamic that the not for profit organization is the league, not the teams that make up the league.
In other words 32 businesses subscribe to one not for profit service to handle affairs among and between them, and to help the 32 units maximize profits.
That's correct. But the OP's comment raises a fair question (though it probably isn't the question he thought he was raising).
The NFL, as a Not for Profit, does not pay taxes on the TV and other revenues, but distributes them to the 32 franchises, which do pay taxes.
That raises an interesting comparison to corporate and individual tax law, whereby a company pays taxes on its earnings as Income and then distributes Dividends to Shareholders, who, in turn, pay taxes again on the Dividend as Income. In the case of the NFL, the taxes are only paid once.
I guess the argument in support of the NFL's Not for Profit status is that the Franchises themselves perform the actions that generate the Revenue and the NFL itself is only a conduit, facilitating the ability of the 32 individual owners to collect income in an orderly fashion.
However, I also guess if one were trying to find a flaw in that argument, one might contend that allowing the NFL to function as a Not for Profit restricts the development of a free market in which each team would be able to cut a separate deal with Broadcast, Cable and other media outlets. In so doing, it might be argued that the NFL's Not for Profit status effectively allows the owners to collude to make Franchise ownership attractive to small market teams while attracting a truly national audience in virtually every corner of the country. New York, Los Angeles, Boston (New England) and other large market teams get the advantage of regional audiences generated by having teams in places like Nashville, Buffalo and other small markets, which still get the same percentage of the overall media pie as do the large market teams.
I'd be interested in the opinion of anyone who practices high level, Corporate Tax Law for a living, as I can see the argument both ways and don't have a stake in either interpretation.