I could only get the abstract of the study since the full thing costs money.
The thing that stood out to me in the abstract was the percentage of women whom reported having had abortions (15%) vs. having had miscarriages (21%). To me the percentage having abortions seems low. From all the statistics I've seen, the number of abortions performed nationally in a certain year is usually higher than the estimated number of miscarriages. In Michigan, our abortion rate is 11.6 (the national rate is probably in the high teens) and yet Michigan's estimated number of miscarriages is only slightly higher than abortions. If Michigan's abortion rate was higher (as it was in the 80's) and close to where the national average is now, then there would be around 20% more abortions than miscarriages. The percentages in the study show the exact opposite with there being 26% more women reporting miscarriages (21,753) than abortions (16,118). Oddly, reporting bias is typically how pro-choice groups try to discount studies which show a link between abortion and breast cancer though I don't know if they've done this by comparing reported miscarriages vs. reported abortions. The lead author even notes in the Reuters article her way of starting with women who didn't have breast cancer was supposed to help prevent reporting bias (though it also would exclude women who already had breast cancer and previously had abortions).
With regards to reporting bias, the authors of older abortion-breast cancer study, which found "among parous women (women who've given birth) a history of induced abortion was associated with a 90% increased risk of breast cancer," suggest the stronger association between breast cancer and abortion in certain regions of Netherlands could be because of reporting bias.
The AP article on the Harvard study includes this paragraph:
What evidence shows is that childbearing before the age of 35 reduces a woman's risk of developing breast cancer, and breast-feeding also helps, said the new study's lead author, Karin Michels of Harvard Medical School. Scientists believe breast cells that have gone through a full-term pregnancy gain protection against cancer, she said.
The article asserts childbearing before 35 and breastfeeding help protect against breast cancer and that breast cells which have gone thru a full term pregnancy gain protection against cancer. Wouldn't the average person after reading that think: Doesn't having an abortion prevent breast cells from going thru at least one full-term pregnancy? Often times before a woman has given birth? If going through full-term birth protects against cancer then wouldn't, at the bare minimum, having an abortion prevent this protection at least until a woman gives birth?