Every medicine has potential side effects including aspirin. Each individual weighs the options along input hopefully from their physician before making a decision on which birth control to use. Lately it's been other methods which have led to blood clots and death.
Cancer has been linked to high fat diets and people still choose to eat fried foods and snacks. Cigarettes have the "warning" on the label stating "smoking has been known to cause cancer" and yet every year teens pick up the habit, In fact close to 500,000 people die a year in the U.S. due to smoke related diseases.
In the big scheme of things "birth control" meds are way down the list of fears for most women. It's been reported that the leading cause of death for women is (heart disease). http://www.womensheart.org/content/heartdisease/he...
"267,000 women die each year from heart attacks, which kill (six times) as many women as breast cancer. Another 31, 837 women die each year of congestive heart failure, representing 62.6% of all heart failure deaths"
Last but not least no one thinks "it" will happen to them. If we calculated the risk on every decision we made my guess is there would be lots of people who would choose not to have children. Seems like autism and ADD are on the rise, more children are having allergic reactions to common everyday foods, in addition there's always a chance a child will be born with down syndrome, missing organs or limbs, heart defect, spinal bifida...etc According to the CDC 120,000 babies are born with defects each year. My guess is every couple who is looking to conceive believes their children are going to be born healthy. My point is most women don't believe they will get cancer from taking birth control pills.