The author makes a lot of good and accurate points, but I also can't help but notice that as his daughter becomes a teenager and is looking to become independent and construct an identity he considers her "mad". All his complaints about his daughter pattern match to reasonably common family situations. I don't mean to dismiss the author's arguments and concerns, but I believe the article reads quite differently if you read it without "picking a side".
According to that article, the author's daughter was diagnosed with autism but the author has decided it is actually schizoid personality disorder.
Her daughter is and has been receiving psychiatric treatment but for some reason it seems like it is really important to her that her daughter be labelled as having a personality disorder or "mad" rather than having some other type of mental or developmental disorder, and it seems like she feels like her daughter is getting the wrong treatment because of this. (I'm not sure I completely understand why she thinks this would make that much of a difference.)
Her daughter apparently wants to do things like spend all day cooking and then throwing the food away and the author feels like this makes her "delusional" for not accepting that this is not something that will prepare her for her future.
Curiously, in the current article the author says that her daughter "almost completely lacks any theory of mind" which seems a bit odd to me because that is something that is usually seen as a hallmark of autism specifically.
In general, I'm having a bit of trouble understanding why the author is coming to the conclusion that the specific problem here is mental health professionals "deny[ing] the existence of high-functioning madness". It's an unfortunate situation though.