WOLSEY: God's death, he means it. That thing out there, at least she's fertile.
MORE: But she's not his wife.
WOLSEY: No, Catherine's his wife... and she's barren as a brick. Are you going to pray for a miracle?
MORE: There are precedents.
Henry wants to marry Anne Boleyn (whom Wolsey derisively calls "that thing") because she's presumably fertile. He needs to produce a male heir to prevent civil war. It's a pretty practical reason to want a divorce and a remarriage. But More thinks that the power of prayer is the only valid solution, since the Church won't grant the divorce. He's treating marriage as a sacrament rather than as a practical solution to problems of state.
KING: […] Thomas, you must consider. I stand in peril of my soul. It was no marriage. I have lived in incest with my brother's widow. Leviticus: "Thou shalt not uncover the nakedness of thy brother's wife." Leviticus: Chapter 18, Verse 16.
MORE: Yes, Your Grace, but Deuteronomy…
KING: Deuteronomy is ambiguous.
MORE: Your Grace, I'm not fitted to meddle in these matters. To me, it seems a matter for the Holy See.
The king insists that he's more competent to interpret the Bible than the Church is—and he's probably sincere in this belief. But, to Thomas, it's simply unacceptable.
KING: Oh, Thomas, Thomas, Thomas. Does a man need a pope to tell him where he's sinned? It was a sin. God's punished me. I've no son. Son after son she's borne me. All dead at birth, or dead within the month. I never saw the hand of God so clear in anything. It's my bounden duty to put away the Queen. And all the popes, back to Peter, shall not come between me and my duty! How is it that you cannot see? Everyone else does.
The king thinks God has shown him something directly, thus rendering the Pope's opinion irrelevant. But in Thomas' eyes, the Pope is the direct spiritual descendant of St. Peter, and his authority on these matters is final. The king is stepping out of his role as a secular authority and into the spiritual realm—the deeper, underlying issue that Thomas can't accept.
KING: I have no queen! Catherine's not my wife! No priest can make her so. They that say she is my wife are not only liars, but traitors! Yes, traitors! That I will not brook now! Treachery! I will not brook. It maddens me! It is a deadly canker in the body politic, and I will have it out.
The king is essentially trying to bully More into accepting his marriage with threats. He's not highlighting the fact that he's breaking with the Church over more than just the marriage—he's causing a fairly major rupture. He's oblivious to More's real reasons for objecting to the move—the greater questions of spiritual authority, going beyond the mere marriage.
CROMWELL: Rich, I know a man who wants to change his woman. Normally a matter of small importance, but in this case... it's our liege, Lord Henry, the eighth of that name. Which is a quaint way of saying that if he wants to change his woman, he will. And our job as administrators... is to minimise the inconvenience which this is going to cause. That's our only job, Rich, to minimise the inconvenience of things.
Cromwell doesn't see Henry's divorce and remarriage as issues of spiritual authority—it's a simpler, practical problem, trying to "change his woman." More sees the issue in an entirely different light, demonstrating how divergent the two men really are.
ALICE: As for understanding, I understand you're the best man I ever met or ever likely to. And if you go, God knows why, I suppose. Though as God's my witness, God's kept deadly quiet about it. And if anyone wants to know my opinion of the King and his Council, he only has to ask for it!
MORE: Why, it's a lion I married. A lion. A lion. This is good. It's very good.
More's marriage is significantly different from the king's. While the king gets divorced and marries Anne Boleyn for reasons related to producing a male heir, we see the intense personal loyalty that More and Alice have. It's not a form of fidelity that would exist for Henry.