I have to say though, if I was an SAHP I would find posts like this annoying. There is nothing wrong with choosing not to work if you don’t need to - but you can’t call yourself an SAHP once your kids are properly at school. In this case, you are a housewife.
I don't get why it should bother me that an at-home parent wants to call themself a SAHP if their children are in school and even less why it would bother someone who isn't a SAHP. Would you like it if someone decided to retitle your role and how you talked about it because they felt something else fit better?
I actually find it more annoying when other people decide this for others because of their own narrow views. I've the really annoying situation of having one of my children's birth certificates being utter nonsense because the registrar decided we couldn't leave occupations blank as we had with our previous and that it was unacceptable for him to be a SAHD if I was no longer employed. He decided not to push for it and just gave her the information she wanted - I don't really blame him, it was a hard time and he just wanted to get home. She literally put in his occupation based on his degree, an area he hadn't worked in years, and put me down as a housewife because I was economically inactive, even though she was told I'd worked recently but left for health reasons and wasn't present as post-birth my health had deteorated further and I was bedbound, but hey, I was a married woman who wasn't working, so I must be a housewife, right?
As likely noticable, it still pisses me off years on that him saying he was a SAHP wasn't respected because of people's view that my being home meant he was no longer parenting - yes he also did freelance when he could at home, yes he was also my carer, yes he also painted and some of those sold -- but he said he was a SAHD and viewed all the rest as just part of his role in the home, much like many of the SAHM I knew growing up, most with school age children.
I'm not sure if my teenager counts as properly in school as he's only in one day a week this year, but I'm an at-home parent. I typically discuss it as 'recovering from significant ill health', because that how I view myself - I don't view myself as a housewife as I don't do most of the housework and I work on and off, some paid, most not, from home so whether SAH or WAH depends on how things are going and how much parenting I do depends on that as well. That's how I see me, how others in a similar situation would define their role will likely be different just like people who WOH can define their roles differently regardless of how their employer does. My spouse's employer gives them a really poncy title, he just uses hotel night worker even when he's managing and training people, that's just how he views his role there. They respect him that much.
To me, this quote reeks of 'Gotta make sure economically inactive women know their place, can't be having any agency to see our role as we see fit if we're not making money, and act like it's insulting to other at-home parents to cover my feelings" when no at-home parent I've met gives a damn about this sort of division.