I think the author is being a bit sensationalist by referring to this as an intuition or "sixth sense"; but it makes some sense that women may be more tuned in to certain things more than men. I would attribute this to any enhanced ability or intuition, but simply a tendency to pay closer attention to certain details. The signs are there for both women and men to read, it's just a matter of who chooses to do the reading. Perhaps social position and treatment have led women to observe certain details more closely.
It is also something of a cultural phenomenon that those "in power" tend to project threatening supernatural abilities into those inferior groups. In Walker Percy's The Moviegoer, a white character insists that black people have a "sixth sense." This is something of a trend in early twentieth-century fiction, and it goes back to colonial humanism, in which colonizers perceived threatening powers in subjugated peoples, deriving from some anti-Christian source.