The political context is the most important. First, the Tudors were not yet a well-established dynasty. This is a key reason for Henry VIII's wanting to divorce Catherine in the first place, he strongly felt he needed a son.

Second, if he divorced Catherine without an annulment from Rome, then he'd have to make his (arch)bishop grant it, lest he not be allowed to marry his next bride. Doing so opens up the possibility that the bishop reject him, and thus risking a religious war.

Third, a minor point that Catherine came with a huge dowry, which was why Henry VII the father of Henry VIII made the younger son marry her when the older son passed away. There was a small possibility that the Spanish may have wanted that dowry back.

So the political consequences were the most important, theology being secondary.

Finally, the Pope or an Archbishop has to have a good reason lest they undermine their own power if they are to grant an annulment to such a public figure. So there was a lot of tiptoe-ing around the key issue, which is dynastic succession.