My interpretation of Allegri is that he's very forward thinking. I think Conte gives him a sense of moving backwards. I think he cares mostly about the UCL and from Conte to Allegri, our chances seemed to increase, so it's a step back for him if we return to Conte.
But Agnelli might also be an intellectually honest paladin and prefers a more modern football. For example, I would believe that Pep is his dream. That's just the impression I get from Agnelli.
(There are other issues with Conte from Agnelli's perspective, namely his unpredictability and instability).