It was not uncommon for kings and princes to divorce. Papal decrees were granted for these, so Henry's case was not a precedent.
His marriage to Catherine had produced no male heirs, and he took this as a judgement from God that his marriage went against Divine Law. He should not have married his brother's widow. There is evidence that he was feeling this way before Anne Boleyn came onto the scene.
Henry openly declared that he and Catherine were therefore having an adulterous relationship, and he must remedy this situation immediately.
He quoted Leviticus, 20:21, in order to demonstrate God's judgement against him, "If a man marries his brother's wife, they shall die childless. He has done a ritually unclean thing and has disgraced his brother." Conveniently forgetting that they had a daughter.
There was a rebuff to this in Deuteronomy 25:5, "If two brothers live on the same property and one of them dies, leaving no son, then his widow is not to be married to someone on the outside of his family; it is the duty of the dead man's brother to marry her."
Another problem was that Catherine maintained that her marriage to Arthur had not been consummated. This could well have been the case as the two were married while very young. For Henry's purposes it was important that Catherine had been fully married to his brother.
The Papacy felt it would be hypocritical to move on this issue as Pope Julius II had given the dispensation to marry in 1509. The Pope was supposed to be infallible, and Clement felt that he was unable to contradict his predecessor.