The way it works is this. Every month, estrogenic hormones stimulate a woman's ovaries to make an egg "mature" and be released. Those same estrogens also stimulate the breast, on a monthly basis. This monthly stimulation going on for year after year *does* form a significant breast cancer risk. If a woman never has a child, assuming she's healthy otherwise, she has a higher risk of breast cancer than a woman who's had at least one child.
So yes, complete abstinence from childbearing throughout life *does* pose a cancer risk. Our "ideal" human pattern (which we don't live out because it's largely incompatible with our economic and social system) is for girls to be married several years after their first period, and to either be pregnant or nursing almost continuously until their forties. In this scenario, a woman will have very few periods - maybe a couple every 3-4 years at most. As it is, women have far more periods throughout their life than nature "intended" for them to have, and there are health consequences.
Is this cancer risk greater, less than, or the same as the supposed risk from abortion? I don't know, because to my knowledge this comparison hasn't been done.