If we're being really fair, it should be noted that the author said the poem was written in jest (although inspired by a stressful night) and that she laughed about it with her husband the next day.
As to those women who were agreeing with her sentiments, I'd want to know whether or not they have to work the next day before I'd be too critical. The author, while not exactly a stay-at-home mom, was on maternity leave and had agreed to take care of the baby at night until her maternity leave ended. So, perhaps the poem is just foreshadowing what she'll be thinking in a couple of months.
The idea that men should help care for the baby of course goes hand-in-hand with the idea that women should be proving half the income.
(Info is all from the link below the video.)