I feel I have to chip in here. My tuppence 'orth is
1. Girls and boys growing up are often very different and don't want to mix. Like single-sex schools, sometimes kids learn better when they are among their own sex.
2. Women-only insurance is offered because there is a statistic that says that women are safer drivers. I think they will insure men, only at a different and higher rate.
3. Women-only swimming and sports sessions are often provided so that women from ethnic minorities can take part without the presence of men which is forbidden in their religions. Also women are often more self-conscious in swimwear and don't want men to be around when they're wearing nothing more than a thin covering of clingy lycra (when they wouldn't normally wear such a thing in public!)
4. At the moment, without sounding like a dungaree-wearing feminist, women still earn less on average, are pushed into lower waged jobs, in some cultures seen as second rate, suffer more domestic abuse, etc etc. I know the tides are changing and one day men will be the weaker sex, but there is still so much discrimination and yes, sometimes it ends in so called "postive" discrimination.
Yes, I agree with Sophie that "they" sometimes make odd decisions about gender divides, but often there are reasons about women feeling inhibited in the company of men, especially in sporting events.
I don't know what my end decision is, but these are the facts I've gathered in working in social policy and some of the reasons why...