This article is flamebait. The title is "Women Aren't Nags", below a big middle finger to the reader, so it's not like it tries to hide it. And much of the article is saying that men are emotionally immature or worse.
For example, she asks her husband to get the house clean for mother's day. He assumes she meant what she asked for, and does a deep clean of the bathrooms himself. But
> What I wanted was for him to ask friends on Facebook for a recommendation, call four or five more services, do the emotional labor I would have done if the job had fallen to me.
But for a single cleaning, just doing it himself was more direct and effective, so what he did isn't unreasonable. But it didn't go through the specific process she didn't mention but was really what she secretly wanted. So there has been a failure of communication here.
Other examples also show similar problems with understanding and communication:
> It was obvious that the box was in the way, that it needed to be put back. It would have been easy for him to just reach up and put it away, but instead he had stepped around it, willfully ignoring it for two days.
One person's "willful ignorance" may be another's blind spot. Some people just don't notice some types of mess. An extreme form of this is sometimes called "clutter blindness" (itself a minor form of hoarding), but it exists in moderate forms too, leading to disagreements like this one. Neither the author nor her husband is in the wrong here, but they both need to do more to understand the other.
And about "emotional labor":
> If I were to point out random emotional labor duties I carry out—reminding him of his family’s birthdays [etc.]
Some people care more about those things than others. Unless he asked her to do that for him, it would probably be fine if she didn't - after all, what would happen if they weren't married? I'd recommend she stop doing it - not as "see how you get along without me!" to spite him, but as an honest experiment that both she and her husband might learn from. It's possible she'd see how his life works just fine without those reminders, or that he'd see how those things are important and start to do them himself.