“Some think, excuse me if I use the word, that in order to be good Catholics, we have to be like rabbits – but no,” he said, adding the Church promoted “responsible parenthood”.
Some took offense, but I don't see why they should. The thing about rabbits is not so much that they have a lot of offspring, as that they're animals, not persons. They reproduce instinctively, without the freedom and responsibility that should characterize human sexuality.
As I read him, the Pope was making mild fun of two things:
A secular caricature of Catholic teaching, according to which the prohibition on artificial birth control is all about the Church trying to grow its numbers, regardless of the wellbeing of women and families.
A rigorist interpretation of Catholic teaching, not unknown in traditionalist circles, according to which NFP is only licit in grave circumstances (i.e. "dire straits"), and really committed Catholics will mostly avoid it, because it's holier to "let God decide" how many children we're going to have.
Liberals aren't the only ones who think that the Church frowns on family planning; many faithful Catholics do too.
They don't realize that Humanae Vitae didn't just prohibit artificial birth control; it endorsed natural family planning. And it endorsed it not grudgingly and hesitantly, but warmly and sympathetically, as a good for marriage.
That's not to say it's necessarily wrong not to use it. It's perfectly possible to make a free and responsible choice to be open to as many children as God sends.
But it's also possible to be irresponsible in our "reproductive choices"—to fail to discern properly what is best for our marriage, for our spouse, for our children, for our society—to fail to make good use of the tools available by God's design out of selfishness or laziness or pride.
Too many Catholics still live and teach as if all the moral danger is on one side of this issue, viz., using NFP without sufficiently grave reasons. I'm glad the Pope has reminded us all that that's not true.