I think the modern attitude towards sex is a problem, but I don't think it's the only problem, since marriage doesn't automatically cancel out any of the underlying concerns here: you can be married and still have severe relationship issues that leads to a woman not wanting the child. Poverty is still a serious issue, not just because families can feel like they have no option but abortion for economic reasons, but because it can lead to abuse.
To a certain extent, I think too strong a focus on the institution of marriage is part of the problem, since we're really just reinforcing the idea that if your relationship falls apart, you don't have anywhere else to turn. The reality is that there are people in unstable situations, some of which are avoidable, but others of which are not. If your solution is to tell people to get in stable situations, you're just going to be perpetuating the difficulties that single, abandoned, or abused women face in the first place.