What’s the logic behind the Elder asking to kill Winston?

Question

I understand when John met The Elder in the middle of the desert, he wanted to find a way for redemption and relive his memories of his wife. I don’t understand why he was asked to kill Winston of all the people? Back in New York he is just serving a 7 day trial to explain the consequences or be replaced by a new in-charge for the Continental.

Did both adjudicator and the Elder decide already to kill Winston for the events from the past irrespective of this 7 day trial? Are we to understand that the Elder has communicated to the adjudicator of his command to let John kill Winston and the latter should oversee this happening? If this is the case when John arrives at New York back from Casablanca why did the adjudicator ask the Asian assassins to kill/chase him before he reaches the Continental?

Answer 1

To kill Winston is to prove to the Elder that John Wick is serious on "amending" his sin. It's not indicated in the movie if the Elder knows that John Wick regards Winston as his friend but do take note about the scene which I will quote

Winston: "I would rather die from a friend"

The point is, John Wick has to lose someone equally valuable and important in his life to regain his right to live.

Answer 2

The elder asks John to kill Winston to prove his loyalty and fealty to the high table (and the elder himself), but makes it clear that until John does this to prove his loyalty, He is still excommunicado. The mercenaries and assassins would have left John alone once Winston was killed, as John would no longer be excommunicated. However, until that time, John still has a 15 million dollar bounty on his head and is on everyones hit list.

The adjudicator did not decide to kill Winston, that's not within her power, and if she had been given the order to kill Winston, he would have been handled the same way as Bowery King, instead of staging a full frontal assault and giving him plenty of time to prepare a resistance. The Elder is the one who orders Winstons death (possibly because he knows Winston has no intention of stepping down), and as the "One above the high table", he doesn't answer to anyone.