It need not be outright abuse for it to be an unhealthy relationship. If your marriage is characterized by constant bickering, or by a partner who stays long hours at work followed by long hours at the bar every day just to avoid a spouse they have grown to detest, there may not be any actual abuse but it's hard to see that as a healthy environment to raise a child in. Unfortunately, these are exactly the kinds of things that are difficult to capture in statistics, particularly the very broad statistics you're discussing.
It's also hard to see why decreased birthrates, delayed marriage, and delayed childbirth are bad moves. High birthrates and family formation early in life are more of an r-strategy. Moving to a K-strategy is better for the children you do have, which is the entire point. As a side effect, maybe young people have to find outlets other than marrying at age 16 and having babies to satisfy their sexual urges, but what's the harm in that?
You could plausibly say that most of the harm, in terms of single mothers, comes from the war on drugs, which affects minorities and the lower classes the most. It's two-faced for conservatives to point at certain communities for having so many children out of wedlock while locking up alarming proportions of their men for victimless crimes and turning them into hardened criminals.
Fundamentally, I think people more qualified to make decisions about their own families and relationships than the Pope, the government, or you and I.