People trying to make the case against abortion should stop saying this. Please.
Second of all, the Catholic Church teaches that abortion is wrong because it is always wrong to directly kill a fetus. No matter what. This means that consequences and circumstances are irrelevant to assessing the morality of abortion. Even to save the life of the mother; even if, without an abortion, the mother and fetus would die anyway. Even if carrying the pregnancy to term would cause grave psychological, physical, or emotional damage or suffering to the mother. Even if the woman was raped. Even if the mother is a 9 year old girl who was raped by her step father.
In other words, the Catholic Church’s teaching on abortion has nothing to do with a weighing of costs and benefits; instead it rests entirely upon the notion that nothing can justify or compensate for ending the life of a fetus. Also, if the debate about the morality of abortion is framed in terms of costs and benefits, I think that those wishing to argue that abortion is always wrong will not fare well: for every woman who claims to have been harmed by having an abortion, there is at least one more who testifies to having benefitted, sometimes tremendously, from having an abortion. For every women who is haunted by grief at her decision to abort, there is at least one more who still thinks her decision to abort was the right one just as there are women who do not think of it at all.
Third of all, it is just bad thinking. Although abortion does not increase a woman’s risk of developing breast cancer, not having children does increase this risk. So, does that mean women should not become nuns? Or that women seeking to become vowed religious should be warned that their lifestyle choice might be bad for their health? Moreover, what if it were determined that abortion actually lowers a woman’s risk of developing breast cancer, should the church then change its teaching? Also, in many parts of the world, and until very recently in the industrialized West, pregnancy itself was very very dangerous. In other words, in general, for the vast majority of human history, it would have been “safer” for a woman to not get pregnant in the first place or to not carry her pregnancy to term than it would be for her to actually give birth.
Finally, since the church’s argument against abortion is not about what’s “good,” either objectively or subjectively, for the woman, attempts to argue that “abortion is bad for women” are likely to be perceived as being insincere.
However, perhaps we should also interpret attempts to prove that abortion is bad for women as evidence of the existence of a sort of discomfort with this aspect of church teaching–as a sort of recognition that church teaching should be about women as well as the unborn, or that there is something amiss when what is good for the unborn is not also good for their mothers.
NOTE: While there is no causal link between abortion and breast cancer, there is a link between racial injustice and breast cancer. While white women are slightly more likely than black women to get breast cancer, black women are significantly more likely than white women to die from breast cancer.