They are a warrior culture with their entire society dedicated to fighting a war against the Shadow, where defeat has immediate catastrophic consequences. They need every able body they can get and the bottleneck in the production of able bodies is uteruses. Protecting the women is absolutely vital to survival of the next generation, and that is why men are raised to see it as crucial to their honor. That trait is referred to as a Borderland trait by Moiraine in her farewell letter to Rand, Borderlanders are seen as good warders by the Aes Sedai, according to Moiraine's conversation with Cadsuane in New Spring (it is not the warrior issue, as other cultures produce skilled and deadly fighting men, who are NOT raised to believe that defending their homeland is the most important thing ever - Borderlander warriors seem less likely to go abroad to follow a sister around; the whole protecting women mindset probably fits right in with what they want in a bodyguard), and we see that the Malkieri have similar attitudes towards protecting women. The sole possible exception might be the Saldean women accompanying their men on campaign, but even they don't go into the Blight, and Davram Bashere seems to think that civil war such as we see in Andor is highly undesirable in the Borderlands, so it might be that taking the women on campaign elsewhere is a limiting factor in war. In other words - you don't fight a war so deadly that you wouldn't want your wife to be there, and you don't go all out in slaughtering your enemy, because you'll end up committing the horrific sin of killing women.