When I first started long-distance running about 6 years ago, I heard many comments, mostly from the older people in my life, about how running was bad for a woman's health. I heard everything from running causes breast cancer to running causes infertility. I always laughed it off because I knew so many female runners and the ideas were so ludicrous.
The only negative comments I've heard about cycling is perceived safety issues (i.e. commuting home when it's dark).
I'm not sure how these myths come about!!