Generally divorce produces a disproportionate benefit (relative to other parties) to women, even when initiated with cause by the husband.
> Or that children don't care about aging parents?
Children become adults and end up with lives of their own (more so than husbands), and if the statistics are to be trusted, generally women who live alone (primarily in the legal sense) past their 50s die faster and suffer more.
> Or that women die sooner then men at 50 and male husbands care about dying women?
I don't know how you extracted that, but I meant that women generally become less appreciated (by strangers) by and past their 50s (and that's charitably, often its 40s), and have more trouble finding and maintaining companionship (and romance, if it's on their minds). For men the curve is basically the opposite, they're unwanted (except professionally) when they're young, and gain social/financial/sexual capital into their 40s.
My point is that accounting somewhat for this imbalance (where women's appeal is front-loaded, and men's comes later) is an explicit purpose of the institution of marriage.
P.S. before anyone gets in a tizzy and starts listing exceptions, note (if it's not already obvious) that I am speaking in generalities here.