It can very slightly increase the risk of breast cancer, cervical cancer, blood clots & strokes. Which sounds scary but if you have no close family history of this type of cancer, blood clots or strokes at a young age & you attend your smear tests then it is still completely safe to use BC. I have close family history of strokes in middle age but the risk is still so low & I get blood pressure checked annually, my doctor isn’t worried at all. Pregnancy actually has a much worse risk of blood clots & strokes and yet people do it all the time and are less negative.
Plus as @monkeybutt63 said, it can reduce risk of other cancers (especially endometrial if you have PCOS). Ovarian cancer is more dangerous than cervical or breast cancer too.