“The last thing the pope would wish to do is support any kind of division,” said Keith Pecklers, a Jesuit professor of Liturgy at the Gregorian University in Rome. That may seem odd. If the Church of England splits, Catholicism stands to gain new adherents. Traditionally minded Anglican priests and bishops—and, in some cases, most of their flocks—can be expected to defect to Rome.
It does seem odd if this is viewed from Rome as "defecting". The report goes on to give one reason for this perspective.
many Catholics have invested time, effort and prayer in trying to reunite with the Church of England, and there have been moments when they dared to hope it was possible.
It appears many of those folks would prefer it not happen if it's not according to plan. While perhaps millions of people would join the Catholic Church, some Catholic bishops would be discomfited.
Good friendships and working relationships have been formed along the way (one is between Rowan Williams and the Archbishop of Westminster, Cormac Murphy-O’Connor).
The paper says there are also what it calls less sentimental reasons for some of the Catholic hierarchy discouraging masses of Anglican's coming into the Church.
the acceptance into the Catholic church of large numbers of married Anglican clerics would make it harder for the Vatican to hold its already shaky line on priestly celibacy.
If so, then again adding many members to the Church is discouraged because of administrative difficulties it would create. This isn't a universal attitude, but it is widespread. (At St. Al's, staff will publicly state that programs and policies are chosen based on whether they involve more work for them.)
There's reportedly another source of opposition.
those Roman Catholics who would welcome a more tolerant attitude towards homosexuality, or the greater involvement of women, could see their cause set back by the arrival of the [Anglican] rebels. “High” Anglicans can be more papist than the pope.
To sum up, there's always the threat that a crowd of converts will bump the thermostat off the lukewarm setting.