One thing self-defense classes always teach is the situational awareness that you mentioned, and also appearing focused on your environment and surroundings, alert and watchful. Predators look for distracted prey -- someone jogging with headphones on, oblivious to everything. Someone digging through their purse or looking at their phone, or walking with their head down and not looking around, in their own little world. If you're doing these things, having a gun in your purse or pocket isn't going to be of much use if you are suddenly assaulted from behind by someone you were unaware of.
My issue isn't with those who think of a firearms in practical terms -- basically just as a tool with specific and limited functions. Rather, it's with those who think of firearms almost in magical terms, as a token of manliness and a totem of protection. They seem to imagine that simply by having a firearm on them, they're automatically safer, when in reality the circumstances where having a firearm on hand would make you safer are pretty rare, and there are circumstances where it would make you less safe, as well.