Interestingly enough, 1996 saw what was then the biggest gender gap on record for a national election (11 points.) It was also the first election in which women were decisive since Dole won narrowly among men (all previous presidential winners, with the exception of maybe JFK - no national exit polls were conducted in 1960, IIRC - had won among both men and women.)
Gallup actually did conduct an exit poll in 1960 - Nixon won women 51-49, while JFK won men 52-48. Gallup started doing exit polls in 1948, but 1964 was the first election in which women were more Democratic than men. Prior to that, I suspect it was because the female electorate was more middle class than the male one - e.g. the influence of labour unions, and the fact that working-class Irish Catholic women used to have notoriously low turnout. 1976 is the only election since where women were more Republican than men.