Today's fallout was very public - Athletic's training sessions are public and there're usually several hundred folks there in addition to the regular media. Apparently during training, there was a practice game between the first team and the cantera. Bielsa stopped the practice game, pulled the first team aside, and started yelling, directing most of his anger at Llorente. And at some point Llorente responded in kind.
A LOT of the players have issues with Bielsa and his training methods. The number of guys who've been out with sports hernia injuries is scary (2 having had surgery for it so far), but that's the most public visible sign apart from Javi Martinez leaving and Llorente refusing to renew. Bielsa's presser about having offered to resign is...good politics but should not be taken at face value. It was a CYA interview. There are also issues between players and club management (Urrutia is a militant hardline Basque nationalist and to him the hint of anything but blind desire to stay with Athletic for life is treason and disloyalty. don't take his pressers at face value either - those in particular are stage managed very carefully). It really is a mess.