Not that I think that wearing a helmet is a particularly good idea - pity that my wife does 🙁
But it's *your* head (and neck).
Just find a report of someone who was strangled by their helmet and tell her you're too scared to wear one in case the same thing happens to you.
Or point out that more pedestrians suffer head injuries than cyclists so tell her you'll continue to wear one for cycling provided she does the same every time she walks!