That is apparently 'strict' catholic doctrine. The catholic church is kind of against anything where you enjoy yourself

.
I think it's a bit of a weird thing to say though to be honest. It's not as if the two are mutually exclusive, and pets are God's children too. Yon Pope fella has been doing and saying a lot of seemingly sensible things so far, it seems an odd policy to bring all that in to question over. The fundamental point may be that children brought up as catholics are maybe more likely to stay catholics, and they're worried about declining numbers in certain parts of the world.