I don’t think it’s an inherently gendered thing, as others have said; though I do think that western society definitely “allows” men to turn their brains off more than it allows women to.

For instance, I like to just turn my brain off while I’m on a walk; but women can’t really do that as they have to be doing constant threat assessment on every man who comes into their field of vision. Over time that sort of thing compounds and trains men that it’s ok to just not think while they’re out and about, while it trains women that they have to have constant awareness.

Another thing is that a women who doesn’t appear to be preoccupied or busy is usually branded as an “airhead” in popular culture, while a man who seems similarly relaxed is called a “thinker.” Another thing that compounds and trains men that we’re allowed to think, but women have to worry.

Also worth noting, women are typically put in the position of caring for others; meaning that their mental consideration (and thus their anxiety) has to grow to encompass those under their care as well. Men, on the other hand, are often relegated to “breadwinner,” which means that they don’t have to think as much about children, aging relatives, etc. (think about the “fun dad/mean mom” archetype you see in commercials, sitcoms, and so forth). This is presented as the default for adult women in western society, which teaches young women from a young age that that’s how they have to act.

All of these combine and reinforce one another, and I think probably result in the gender disparity you’re talking about.