Above: The Shrine of St. Thomas Becket at Canterbury Cathedral, where he was struck down by Hugh de Morville and others walking to Evensong. (Some modern art style has to wreck a Medieval Gothic Church.)
We pick up with Eliot's Murder in the Cathedral with the third knight, Hugh de Morville. He enters the front stage to give an account of why he participated in the killing of St. Thomas Becket. We will find the following ethical theories espoused:
Violence for the sake of Social Justice (the literal "Social Justice Warrior")
Hugh: I am going to appeal not to your emotions but to your reason. You are a hard-headed sensible people, as I can see, and not to be taken in by emotional clap-trap. I, therefore, ask you to consider soberly: what were the Archbishop's aims? and what are King Henry's aims?
Here he appeals to "reason," but we haven't seen what he means by "reason" yet. Whose reason? This is an ancient rhetorical strategy to make you dispositionally open to what he's saying, lest you tacitly be perceived as being "unreasonable." He actually is playing on emotions, on a desire to seem rational to him. This hands him over the authority to determine what counts as "rational."
Hugh: The King's aim has been perfectly consistent. During the reign of the late Queen Matilda and the irruption of the unhappy usurper Stephen, the kingdom was very much divided. Our King saw that the one thing needful was to restore order: to curb the excessive powers of local government, which were usually exercised for selfish and often for seditious ends, and to systematise the judiciary. There was utter chaos: there were three kings of justice and three kinds of court: that of the King, that of the Bishops, and that of the baronage...Had Becket concurred with the King's wishes, we would have had an almost ideal State: a union of spiritual and temporal administration.
An appeal to consistency isn't enough. An archer who misses the target every time is consistent, but still a terrible shot. So is a cook who burns dinner every night. A system or order build upon evil consistencies is not only irrational in that it has no foundation but claims to stand, but no one wants this deep down because such a government doesn't fulfill the purpose of government.
Second, the desire to "restore order" seems rational and just. But whose account of order? Why if one person thinks The Church should be the arbiter of Faith and Morals and the other thinks it should be The State? His account of chaos, disorder, and selfish behavior is all correct. However, it leaves us with the question, "Given The State is in disarray, are you suggesting murder is an acceptable means to the end of restoring order? What Sir Hugh believes is "rational" is "the end justifies the means." Once you accept that, sure, murder is fine.
Sir Hugh de Morville here acts as a Utilitarian. He believes in "the greater good" rather than "The Common Good." He appeals to ends, consequences, "getting the job done," or "you gotta' break a few eggs to make an omelet." Most of us practically don't believe this once we start suggesting awful potential means, e.g. sacrifice one innocent to save a hundred, butcher your neighbor's dog since you need breakfast, kill millions in death camps for medical progress, etc.
Second, there's a logical problem. An end consists of its means, and good and evil are logical opposites, so it can't be that evil means "add up" to good. It just "adds up" to a contradiction. The metaphor of addition here is linguistically misleading as if an "unmarried bachelor" was really "unmarried" and "bachelor" adding up to something, rather than simply a no-thing qua contradiction.
Utilitarians typically think of themselves as "practical" and of their opponents as "idealists." I.e. if you're not Utilitarian, then you're a Kantian. From the Catholic perspective, the ends don't justify the means so the Utilitarians are wrong. Likewise, there are certain laws that can never be broken, but there are rules that exist for times and purposes that may be suspended, refined, or removed altogether. E.g. The Dogma of The Holy Trinity cannot change while clerical celibacy may allow exceptions such as with Catholic Priests who are married and in The Ordinariate.
In short, Mr. Hugh de Morville, finds another way to bring about good that doesn't include doing evil. Anything that draws you further away from God is the most impractical thing you could do. No State will exist in The New Heavens and The New Earth, so to subordinate the fate of your soul to whether or not The State is doing fine by its own standards is quite impractical.
Last, his perfect unity between temporal and spiritual powers isn't a unity with each taking its proper purpose, it's really The Church submitting to the State on matters of Faith & Morals. But this is a begging-the-question fallacy for S. Becket because he stood up to them because he thinks The State has no authority over Faith & Morals!
Hugh: The moment that Becket, at the King's instance, had been made Archbishop, he resigned the office of Chancellor, he became more priestly than the priests, he ostentatiously and offensively adopted an ascetic manner of life, he openly abandoned every policy that he had heretofore supported, he affirmed immediately that there was a higher order than that which our King, as he as the King's servant, had for so many years striven to establish; and that-God knows why-the two orders were incompatible.
Here Sir Hugh appeals to our own spiritual Sloth. He hopes as lazy Christians we'll hear "asceticism" and think of ridiculous, mean-spirited fasting, abstaining, or practicing mortification. We'll hopefully think, "My goodness, so Medieval!" and excuse ourselves from those barbarous practices. Our need to not practice The Faith then will rest on our belief that The Fall didn't really hurt us all that bad, right? We thus shall not believe in repenting, in changing our mind. Once we believe that, the idea that Thomas Becket worked so hard to establish public policy only now to change his mind will seem ridiculous to our ears. Becket will seem a madman. Lastly, we're exhorted to understand that violence is the only way to deal with such madmen. Now you see how the rejection of one doctrine becomes a landslide unto rejecting others. If you bite onto Sir Hugh's logic for a second, he's got you hook, line, and sinker. Catholicism is also a package deal, take the whole or leave the whole. This ain't a buffet.
In regards to the "incompatibility" of the two orders: the classical expression of Church-State relations is that The Church is the authority over Faith and Morals, and only over civic matters insofar as it is necessarily involved with ecclesial matters. For an example of this last caveat, say a King practices usury, tortures his citizens for fun, and sacrifices children for a successful season. The Church could declare he has contradicted Natural Law, and thus declare that rebellion would not be disobedience. This is extreme. From day to day her limitation to Faith and Morals means she doesn't go about arresting, taxing, or executing people.
After Henry VIII the Anglican theologian John Hooker wrote The Laws of Ecclesiastical Polity to defend the position of The Church being subordinate to The State even on matters of Faith and Morals. This position became known as Erastianism after the Swiss theologian Erastus, who Hooker knew. Now imagine The Church trying to say to a Christian State, "Look, Jesus taught on divorce in Matthew 5 and 19" only to have The State say, "We will decide what morals are true." The Church could try to make a Natural Law argument on marriage at this point but imagine a Henry VIII type saying, "Ehhh...I sorta' want to get divorced. So we're not doing Natural Law either. It's just my will, and I am The State."
Modern Erastianism exists frequently in Christians who wish to "serve" but implicitly come to mean "The Church exists for The World, to serve her, to make the world better, etc." The idea of Christians serving The State just to make the world better implies The Church exists for the world. But this contradicts Catholic Doctrine:
Christians of the first centuries said, "The world was created for the sake of the Church." God created the world for the sake of communion with his divine life, a communion brought about by the "convocation" of men in Christ, and this "convocation" is the Church. The Church is the goal of all things -The Catechism of the Catholic Church, #760