To continue the massive detail about toilets...
Men are a threat to women (and to other men). Single sex spaces allow women space away from men. This helps lesson the possibility of assault (e.g. there is significantly more sexual assault in mixed sex changing villages than in single sex changing rooms), but perhaps more importantly when it comes to toilets (in the UK at least) single sex toilets provide an everyday single sex space where women can be sure (or should be able to be sure) that men are not present, allowing them to maintain privacy and dignity when they are vulnerable because of their physical body.
This thread is good on toilets: www.mumsnet.com/Talk/womens_rights/3203454-What-do-you-use-the-womens-toilets-for
Clara Greed is also good on toilets.
Of course their are plenty of places in the world where women really are at risk of sexual assault by men just because they are going to the toilet, which is why the UN
advocates for single sex toilets for women, prescribing their layout down to setting out how entrances should be oriented in order to reduce the risks to women.
Unpleasant behaviour by men towards women doesn't have to amount to sexual assault to be very negative for women - voyeurism, harassment, intimidation for example (think of the epidemic of cameras in loos in South Korea just for kick off), but much of it is difficult prove, many women would feel silly about being bothered by it and most women would just get out of there as soon as possible. Just the presence of a man in a woman's space could be a red flag, On the basis that that man clearly doesn't understand boundaries.
The question for me that really need answering are, why do we have single sex loos in the first place and what advantage is there to women in opening up their loos to any man ho wishes to use them?