Interestingly enough, Galileo is a more apt example than you might think at first - like this situation, his trial and house arrest were a murky blend of religious doctrine and practical politics. It wasn't just that he was publishing and advocating heliocentric doctrine, but the strawman in his book representing geocentric believers - named Simplicimo - directly quoted the current Pope in a few arguments, thus indirectly making the Pope (who could, in the 17th century, order your head chopped off) look like an idiot. (also, it was 300ish years, not 500, and they stopped enforcing the ban centuries before JP2 owned up to them being wrong, but that's not relevant to the topic.)
The parallel here, in this case, is the recognition that the world and their own constituency are changing against traditional doctrine, clashing against the internal political workings of the church. The initial statement was revoked to keep the conservative bishops happy, with some liberal bishops thinking even the original draft was too conservative. There was a mention in-article about this synod being 'open', compared to previous ones were entire topics were quietly declared verboten. The RCC may not be a literal nation-state anymore (well, the Vatican is legally, but meh), but it still has incredible wealth and tremendous influence all over the Western world, particularly in South America and parts of Europe. Changing too rapidly or too radically would threaten the secular influence the Church by alienating their base, which ends up being factored in to the whole equation.