I think Coach B made it clear to Hauck over the past few games that he was increasingly frustrated with the poor communications, blown tackles, lack of a pass rush, failure to get off the field, few turnovers and TFLs, penalties, and failure to show much improvement while the season was slipping away. For his part, I think Hauck had difficulty relating to today's players, was not used to coaching at the P4 level, and did not like being criticized by a younger head coach after calling the shots for so many years as the HC. Hauck figured he didn't need the aggravation, and at least had the sense and class to resign after seeing he would not succeed at Illinois. Coach B looked relieved to move on, and pointedly did not thank Hauck for his service to the program.
Both are happy to be done with this totally failed experiment, though I expect the Illini to retain Hauck's old DC and the 3-5-3 D for the rest of this year, tweak QB pressure packages, emphasize better tackling, swarming to the ball, taking away the opponent's primary weapon,and streamlined communications. Retooling to a whole new defense at this point and issuing/learning a new playbook, has no advantages and would likely cause complete confusion and tank the season.