Here’s the thing — even if you only do this type of thing (change her battery) once a year while she does her laundry list of childcare things every day, it’s a false equivalency.
If she didn’t have a husband, how much more would she spend on AAA, or on mechanics? Maybe it takes you 5 minutes to change a spark plug, but that is actually saving her 2 hours of taking the vehicle in to the mechanic and 2 hours of earning the money to pay the mechanic?
Also, the author talks about female anxiety (do the kids have their lunches, etc.) without talking about male anxiety — many men, as the primary breadwinner, feel the burden is on THEIR shoulders. I know families where the father worked 2 jobs while the kids were little so mom could stay home with the kids. (When the kids got to school age mom went back to work in some cases, in others by that time dad had gotten a promotion, etc.) If a burglar breaks into the house, it is assumed that dad will be the one to confront the guy to defend his wife and kids.
I have no issue with men taking on these traditional burdens, but the flip side of that is that women take on additional burdens in other areas — maybe they do a lot more of the child care when the kids are sick, for example, and they are the ones buying presents for his mother on mother’s day, etc. Instead of griping about this kind of stuff, both men and women need to step back and look at the whole picture.