This report from Sustrans - while nothing very startling to many on here, I suspect - is unusual in being based on a decent survey sample and some in-depth interviews with women who both do and don't cycle, backed up by the current research
As nobody will be shocked to learn - while many women do cycle and are fully aware of the benefits to their health, bank balances and so on, many face a mixture of barriers, including the need to ferry children, making more complicated trips ('trip chaining') outwith peak hours (which affects their ability to include public transport in the mix), greater fear of dark and lonely places at night, greater risk aversion and reluctance to mix with traffic, more time pressure (yes, we know cycling can often be faster but it isn't always and also non-cyclists may not realise this), and for some, a greater need to look smart at work than, on average, men.
Each one of these barriers is no doubt surmountable - indeed many women already surmount them - but they do add up, and this is a good reminder of what they are, for the next time someone breezily suggests that a bit of confidence training and a pretty helmet is all that is needed.
Interestingly, women do walk more than men, take more public transport and, despite lower cycling rates, drive less than men so perhaps the next time we have one of these gendered debates it can be along the lines of 'why do men drive so much?' rather than 'why do women not cycle?'