In her seminal work, The Continuum Concept, Jean Liedloff presents the

AdityaHongunti , this kind of passage can be incredibly frustrating.

We have to reason "backwards" a bit. The answer to the primary purpose question in this instance depends on
1) POE, and (2) reading between the lines to find inconspicuous but marked difference in the way the author
presents the parties in the controversy.

Because the author tilts the narrative in defense of Liedloff's theory. The way the author depicts Liedloff's critics,
they might as well hang themselves with their own ropes.
This author is not merely reporting two sides of a story.

Certain words that describe positions or outcomes; whatever is not said; and who gets the last word
are just three ways to ferret out an author's point of view. This kind of RC question is among the hardest. I am not surprised by the stats.

Oddly enough, your description comes very close to the correct answer. You would prefer
that primary purpose be "presenting a work and substantive arguments made in support of the claim in work."

The author does exactly what you say, except that the "presentation" is not neutral. The author does not
explicitly mention support. But the way the author depicts each side suggests support of Liedloff.

Structural elements are one giveaway.
• Liedloff's approach is supported by research. Her critics' work? We don't know.

• Liedloff exposes the critics' method as emotionally indifferent at best,
cruel at worst, and tilted toward power rather than psychological health.
The author chooses the words that constitute Liedloff's critique. The author does not soften this depiction.

• Liedloff's critics then look even worse when they charge in bombastic language that her method
does not employ "natural hierarchy and dominance," does not "bend[] the child's will . . . from the moment of birth" and thus does not or cannot
teach children right from wrong.
The critics sound inhumane and authoritarian. A newborn? From the moment of birth these folks are interested in control and dominance?

In addition, in paragraph 4, critics have no response to charges that they produce damaged and dependent adults.
Rather, they assert that Liedloff's method fails to produce adults who know right from wrong.

The author gives Liedloff "airtime" to shut down that avenue and to have the last word.
To the contrary, Liedloff reasons; a child who lacks choice never learns to rely on an inner compass to decide what is moral.

What does the author NOT say? Well, this author does NOT say anything positive about the critics' theory.

Outright mention of support of Liedloff's alternative view is not necessary.
The author, as you phrase it, "almost explicitly mentions supportive notions."

Key? "Almost." In RC, tone is muted. Strong phrasing is a tip-off.
True, the author is reporting Liedloff's work, but the author chooses the words.
The author describes Western children as "[v]ictims of emotionally barren parents."
In RC, such phrasing is tantamount to megaphone announcement that the author
does not intend to portray the other side in more neutral language.

As soon as I saw "victims of emotionally barren parents," I was on the alert to look for a similarly loaded phrase
about Liedloff's approach. There is none. That phrase thus is illustrative; the passage is not neutral.
Argument structure, evidence, tone, and reasoning (or lack thereof) tilt heavily one way.
The author supports Liedloff.

Pick out some other words that the author uses to describe the critics.
None carries a positive tone. Finally, although Liedloff's work is controversial,
it is also seminal: very important, not to be ignored, and path-breaking.

Question #1: Process of elimination

1. The primary purpose of the passage as a whole is to
A possible trap. Paradox is strange, as are self-defeating child-rearing practices.
Careful, though. The word strange is not strong or specific enough, especially compared with (E).
Paradoxical parenting practices might be "strange," but the author's presentation of Liedloff's scathing critique
goes well beyond description. Eliminate A
In left field. (Far removed from the passage.)
The author of this passage is precise and descriptive. The test taker may think that the notions are vague,
but the author never suggests that the notions themselves are vague. Eliminate B.
Condemn is much too strong a verb for most RC questions.
Further, we have no idea what information her critics rely upon to form their opinions. Eliminate C.
This answer could be tempting. Liedloff certainly has argued against what she thinks are "wrong ideas."
But the author is more subtle. The author's primary purpose is not that he or she will directly refute the misconceptions.
Eliminate D. (That, or keep and compare to E. In the latter case, (E) wins.)
-- This answer is correct, although perhaps not straightforward because the author
uses structure, not explicit words of judgment (save one, "seminal"), to "support" Liedloff's theory.
-- The theory is indeed "alternative." Liedloff's belief that Western parenting methods are counterproductive is "controversial."
Liedloff and her critics are presented in contrast throughout the passage.

If a reader still is not convinced, think about the use of babies as an illustration.
Liedloff's approach to babies lies in stark contrast to supporters of Western methods.
Western babies and children are "alone most of the time" and "left to 'cry it out'."
Liedloff's prescription is indeed an alternative: parents should respond to children physically
and should create a psychologically safe environment. Her critics do not talk about psychological anything.
-- Does the author "support" Liedloff?
I would say yes, without question.
The author spends most of his or her time presenting Liedloff's views in a way that suggests defense of those views.

The critics do not really have an answer to anything Liedloff says. Their retort (authoritarianism is good)
feeds right into her critique.

You mentioned Mike McGarry's approach to point of view.
I just found one post that I think will help.
In this post, see GMAT Reading Comprehension Question Type 6: Author’s Tone.
This quote made me laugh and shake my head knowingly


Answer E is the best of the five.

3. Which of the following best describes the function of the passage's fourth paragraph?
I suspect that this passage really has only four paragraphs, and that what are now
paragraphs 4 and 5 should be merged into what would be the "fourth paragraph."

If someone has a copy of Princeton Review, take a look.

If I am correct, the answer to question 3 is (A). Even if I am not correct, the answer is (A.)
Regardless of structure, not one other answer is in the ballpark, let alone in left field.
(A) It provides the reader the opportunity to see how both Liedloff and her critics rebut each other's opinions. Correct.

B) further testing and research? There is no such statement.

C) suggestion that Liedloff's theories are incomplete? There is none.

D) stressing need for authority? NO. That's what the critics SAY, but if anything,
the author caricatures this stance.
Goodness -- look at the words: natural hierarchy, clear dominance of parent over child, and
requiring the child to bend to the will of the parents from the moment of birth.
The author does not endorse the critics' view.
If paragraph 4 is a standalone, it is a foil that Liedloff uses in rebuttal in the fifth paragraph to get in the last word. That's (A).

E) suggestion that Liedloff will modify her methods and is not scientific? No such mention.

Generally
The passage is mostly well-written. The author employs fairly sophisticated and subtle devices
to convey an overall tone of support for Liedloff. Such devices are common in RC.
By contrast, in CR, POV is usually clear.

On closer inspection, the way the author presents the contrast between Liedloff and her critics
is both unflattering to the critics and unobtrusively supportive of Liedloff. This material is difficult.

I hope that helps.