A former classmate, now a prof at Penn State, once conducted a study of dads of working moms and found that “sensitive new-age guys” contributed something like 15 additional minutes per week towards household labour, relative to more traditional types. I suppose that’s not nothing if it is 15 minutes of critical, rather than meaningless, work (such as responding “Yes” to “Can you just stay with the kids in front of the TV for a bit while I go scrub the toilets?”), and I’m glad to see that some of us have moved in a more equitable direction, but overall progress is not huge.
I would think, as well, that when it comes to allocation of household labour, one of the considerations is what the financial impact of shifting more to mom or dad (even where there are two moms or two dads) will be. To the extent that women may not be compensated as well as men for similar work, you can see where the typical reasoning might be that it “makes more sense” for the partner whose earning power is compromised less to assume more of the burden of household labour, which may or may not include child-rearing or tending to frail family members. Wage discrimination is partly what sustains gender-role in the workplace, and slow movement on family-friendly policies. I’m not saying I support that view, or that it does not emerge out of gender discrimination, merely that it happens.
Conceivably, employer policies may reflect that strategy, presuming that one category of employee does not require family-friendly policies because they forfeit very little by taking time for family responsibilities, and another category does not require them because they don’t have to tend to such things. Essentially, there are gender-role assumptions on the part of both employees and employers, which is probably why things don’t change very much.
Back when I used to teach gerontology, I know that one of the more intriguing findings was that men tended to experience less caregiver burden and stress with frail parents than women did (and bear in mind that “less” is not “none”). The basic reason was that adult sons had an ace in the pocket of feeling that they could always hire outside help if need be, where adult daughters felt that it was their responsibility and theirs alone. Sons had an escape hatch, where daughters were boxed in. Perhaps that has changed in the intervening 20 years, but I suspect not.