There was precedent. Eleanor of Aquitaine was granted an annulment from the King of France after the two had been married for years, and had several daughters. (A situation similar to Henry and Katherine’s)

But, (as with most political things) it was more complicated than “we’ve done this before, here’s your annulment.”

Henry was hoping that the church would grant an annulment because Katherine had already married his older brother, Arthur. If Katherine and Arthur had had marital relations, then Henry and Katherine would have been considered like siblings. So in order for two to have been married in the first place, they had to apply for special permission from the Pope.

At the time, both Katherine and Henry swore that Katherine and Arthur hadn’t consummated their marriage (both of them got sick shortly after the wedding. Katherine recovered, but Arthur died).

Later, Henry’s official reasoning for the annulment was that Katherine had actually consummated the marriage to Arthur, and that was the reason that she and Henry hadn’t had a son (which he needed, politically. While personally he was also interested in another woman. A woman who made it very clear that she would not be another man’s mistress.),

He hoped that with the backing of the major church leaders in England, he might sway the pope. His letter to the pope had seals from so many church officials, they had to stick them to ribbons that trailed off the bottom of the document.

He knew what he was doing. Before Arthur died, Henry was studying to enter the church.

Katherine (who was resigned to looking the other way when Henry took a mistress) fought the annulment the whole way, which made the process less likely. Especially since her nephew was the Holy Roman Emperor Charles I, who had tremendous influence over the pope. (Remember, she was deeply catholic, deeply religious. Henry’s divorce wouldn’t just take away her crown and her daughter, it would also demolish her reputation, and her standing with God.)

Part of the reason Henry couldn’t just divorce or behead her was that she had powerful allies outside of England.