Ms. Anscombe is a smart woman; this was written in 1977, however she offers us insight into the human heart, not just the legalistic points of living the moral life. She speaks from her own experience as a convert and as a mother and wife.
In the beginning of her paper, she introduces what she calls the "contraceptive morality," an attitude that was beginning to take shape during her time in which women were being sold out as objects due to the availability of somewhat-effective contraceptive measures and ultimately availability of abortion services.
In the first part of her paper, she says the following with regard to the true reasons of the human heart for choosing chastity over contraception.
Against the background of a society with that [contraceptive] morality, more and more people will have intercourse with little feeling of responsibility, little restraint, and yet they just won't be so careful about always using contraceptives… Now if this - that you won't get this universal "taking care" - is the only objection then it's a pretty miserable outlook. Because, like the fear of venereal disease, it's an objection that's little capable of moving people or inspiring them as a positive ideal of chastity may.
When contraception is chosen over chastity, the purpose of marriage is clouded by selfishness and pleasure, in lieu of its first purpose as an environment suitable for the procreation and education of children.
More to come on this fantastic paper later!