Why did T. S. Eliot write Murder in the Cathedral?

Murder in the Cathedral by T.S. Eliot is a drama based on real-life assassination of Archbishop Thomas Becket in Canterbury Cathedral. The play is derived from the eyewitness account provided by Edward Grim.
Eliot wrote this play for the yearly Canterbury Festival in Kent. When Eliot wrote this play, Europe was dealing with the growing tensions brought about by fascism.
The play talks about the conflict between duty and conscience. Thomas Becket was appointed by King Henry II as the Archbishop of Canterbury so he could help quell the growing opposition to his reign. However, Becket took the side of the opposition.
Conflicts erupted between him and his former friend, King Henry II. Facing the possibility of death, Becket deals with the four tempters.
The first tempter offers him safety: “Take a friend’s advice. Leave well alone.”
The second tempter offers him power: “To set down the great, protect the poor, Beneath the throne of God can man do more?”
The third tempter offers alliance with the powerful to overcome the king: “ In fight for liberty. You, my Lord, in being with us, would fight a good stroke.”
Lastly, the fourth tempter who advises him to become a martyr: “You hold the keys to heaven and hell. Power to bind and loose: bind, Thomas, bind.”
Becket answers the tempters by saying, “The last temptation is the greatest treason: To do the right deed for the wrong reason.”
After eight years of conflict, Becket is killed by four of Henry’s knights in the church.