Though many parents may be convinced of TCS in theory, they often want practical advice on how to resolve real problems; yet, as TCS parents come to learn, there is no one solution to any given problem just as there is no one kind of child or parent.
This is ambiguous. The passage could mean that because finding a common preference does not depend on solving one particular problem, but rather any of many, there are many ways to find common preferences. But the passage could also mean that single problems have multiple best answers -- that truth is pluralistic (I won't go into my objections to relativism here, but I will suggest that TCS follows Popper in opposing it, and so should TCS writing).
Additionally, in my interpretations lies a mistake! They use the hidden premise that the passage means something logically coherent. there's no particular reason to assume this. a better theory is that it's supposed to mean some combination of my two suggestions, and some other stuff as well, and that these meanings aren't all that consistent
Unlike most approaches to parenting, TCS does not and cannot offer formulas or methods for dealing with specific problems. This is because finding common preferences involves discovering what is most preferred by the very unique individuals involved.
The first sentence is misleading. Although there is a school of TCS thought concerned with constraints on how to parent, it is certainly not true that TCSers cannot or should not make tentative conjectures about specific things to do with either their children or most children. In other words, although TCS does not have a list of The Golden Methods that all parents must use, it is also not true that whenever TCS parents find methods of dealing with things they go "oh my god! a method! i better not use it!"
to get a sense of methods... washing the counters first and mopping the floor second is a method of cleaning. and rather a good one, cause of drips. now, TCS doesn't say all people must clean this way. maybe someone will figure out a better way later, or whatever. but a parent who uses this method is not barred from being TCS.
The second sentence is, to the extent the first is true, not the reason for that as it claims (note word 'because'). Additionally, finding common preferences does not require finding 'most preferred' things. Nor even is finding what people want a main part of CP finding. Generally, we have some idea of what we want, and CPs are found by a combination of figuring out how to get what we want and figuring out how to change what we want. Although sometimes we'll have what we want wrong, and find analysis in that direction helpful, it isn't part of the general method of CP finding.
Calling the individuals involved 'very unique' and the rest of the sentence gives the impression that the world works something like: there are different people, each unique, each special, each important. To live in harmony, we must find the natural, most perfect things for each to want and do. And by getting in touch with our inner selves like this can we solve most/all problems. This vision is wrong.
That's a hard truth for new TCS parents.
and followed by more meta and then three scenarios. the scenarios are riddled with errors. but i can't be bothered to point them all out without a stronger conviction that anyone cares. if any readers really want to find some of the errors, and try themselves, and don't see them, feel free to ask questions in comments. preferably fairly specific ones.