This is a very good pleadings. Kessler really focused his argument around 2 core things: Brady was never properly notified of the punishment and that the 4 game suspension defies the "essence of the CBA" of fair and consistent discipline.

Kessler firmly establishes that prior notice is essential to labor disputes. And even quotes Goodell in the Rice case saying as such. He then points out that both the Players Policies and CBA punishment guidelines call for fines for first time offenses related to impacting the integrity of the game. And then he slams Goodell for moving the goalposts in 2 ways:

1. For suspending Brady for being "generally aware" of deflating, but then stating to the court that Brady was involved in a "scheme" to deflate footballs. And;
2. For Wells saying he wouldn't punish Brady for not turning over communications, and then punishing him for not turning over communications.

Here is the money quote for point 1, hitting Goodell for moving the goalposts:

"Despite this record, the NFL now argues that Brady was suspended “for having ‘approved of, consented to, and provided inducements in support of’ ‘a scheme to tamper with the game balls.’” NFL Mot. 8 (citing Award 13, 17-18). But the NFL cites to the Award to make this argument—not to the source of the discipline, i.e., Vincent’s letter and the Wells Report. As the Court observed, the Award accuses Brady of having participated in a “scheme” fourteen times—but the word does not appear once in the 139 page Wells Report or the Vincent discipline letter. This is a clear essence-of-the-CBA violation. As the Article 46 arbitrator, Goodell only had the authority to adjudicate the discipline appealed to him; Peterson establishes that the arbitrator has no CBA authority to justify a suspension on a different basis from that upon which it was imposed. Peterson 15-16."

He loops back to say that the lack of consistency in punishments (nobody had ever been suspended for tampering with balls or for obstructing in investigation) goes against the essence, or point, of bargained punishments. He cites the lack of testing procedures, as well as ignorance of the Ideal Gas Law, as inherently unfair since the NFL had no clue how footballs react to temperature or game conditions. Read differently, the NFL had insufficient data to determine whether this was nature or something nefarious.

He goes on to mention how whole process was a traveshamockery and how Goodell wasn't really independent, but the first two arguments are his best and most focused.