Well, they were partially right. Most women still do not have to do the nasty things, and are not called out as cowards. As you say, 'coward' is an insult only for men. Call me a coward, I'll just grin and try to look cute so you won't hate me. Call me a slut, and you've hit home.

Men evolved to take risks in order to achieve status and therefore the possibility of procreating. As Stefan Molyneux once explained it, giving a white feather to men and boys during WWI was akin to killing them because it meant they were judged unworthy of being mated with. Better to risk death and maiming on the battlefield than experience the sure death of women's sexual shaming.