Here's an issue I've never seen discussed (which doesn't mean it hasn't been discussed). As is well-known, bishops have no compunction about engaging in elaborate schemes to conceal the sexual activity of priests. And the news coverage is focussed on homosexual priests.
However, you also have straight priests. I don't know if they're in the majority or minority. Of the total number of straight priests, a percentage have affairs with women. Or trysts with prostitutes.
The question this raises is what bishops do when a priest impregnates a woman? A parallel question invokes a pregnant nun. How do you keep that a secret?
In the case of a nun, her superiors might instruct her to give the child up for adoption.
In the case of a woman whom a priest impregnated, hush money is a possibility. Say a one-time lump sum payment to make her go away.
However, the safest and most cost-effective way to conceal an unwanted pregnancy would be an abortion referral. Does the policy of mandatory celibacy facilitate abortion? Do bishops avoid the scandal of pregnant nuns or women impregnated by priests by discreet abortion referrals?
I've never seen this discussed, but since there are undoubtedly children conceived in this situation, the question of what happens to them is inevitable. Clearly something happens to them. It's not that we don't hear about it because no such children are conceived. Rather, we don't hear about it because measures are taken to keep that under wraps. Do such measures include abortion?