The first is practical: there aren't enough Catholics in E&W who use the Internet as part of their Faith. It means that we get a few hundred signatures to a petition, which enables opponents to dismiss our views as representative of a minority only.
The second is that by putting up a petition we accept that the game is won by numbers: we are accepting the premise that if 100 people sign one petition and only 50 another the first one has earned some form of superiority.
The Bishops have made a wrong decision; even worse, it may be that they are wrong and are teaching wrong doctrine: I don't know enough to know.
But I know that signing a petition won't change the decision they've made: it will simply move the debate to "Do we obey Bishops or do we obey wild-eyed bloggers on the Internet?" and the result will confirm the "rightness" of the Bishops' initial decision.
Fr Ray's reason is holier than mine are. So there are two practical and one holy reason not to sign.
There is no reason not to oppose, though.
The Pope's visit feels like an opportunity made in Heaven.