With Sanchez digging his heels in and determined to go, only a fool would hold him to his contract, and lose £50m by having a demotivated player for another year, one who dragged the team to an FA Cup trophy, and the heady heights of 5th whilst others coasted through the season.
£50m is a very good deal for Arsenal, and it would be in their best interest to let Sanchez go, and reinvest the money on someone like Mahrez ( at Wimbledon today, so who knows...)
Sanchez is entering the final few years at his peak, he wants CL football, and to play under a manager who he respects totally, and knows he will be surrounded by a motivated top quality in the squad.