Well, I'm pretty sure Conte had no use for Del Piero anymore. And realising that, if he's at the club, you can't keep him on the bench all the time (especially not when results aren going your way) it was best for all parties involved to part ways.
The supposed rift between Agnelli & DP is based on nothing, if you ask me. But the media obviously did their best to make the most out of it. Something they still try now from time to time, but it's not really sticking anymore with most fans. Would have been a different situation if we'd been in 5th position & out of CL by the winter break.