Why would he admit it if he did nothing and they have nothing on him?
Goodell can't relent at this point, for fear of losing face. I think they were hoping Brady would roll over as Kraft did previously, but it's becoming painfully obvious that isn't going to happen. It may be that negotiations were another empty "good faith" exercise by the NFL and the judge. "Listen, just cop to it and we'll lower the suspension and we can move on." Neither side is backing down or giving an inch.
At the feast of ego, everyone leaves hungry.