I cycle in Cambridge which is probably one of the places that is closest to 'Copenhagen' style riding. Sit-up-and-beg bikes with a massive basket seem to be all the rage for teenage girls, for example. Here women DO cycle, within the city, and various kid-carrying bikes are a common-ish sight. We have no hills, which I think helps. Many bike shops dotted about so a mechanical isn't a big problem - you can just push the bike to the nearest shop. The major problem here is theft - pretty much everyone has had a bike stolen (me included) and having a crappy bike is no defence.
The thing that stops me riding is ice. Cambridge council seem to have given up on gritting completely, and they never did the cycle paths anyway. This is not a female-specific issue of course. But it is an issue which means no one will ever say - I won't use a car again, I will ride all the time. Today, for example, I couldn't. And in a cold winter that could be a day-by-day decision for 4 months.