you learned that the tooth fairy doesn't exist

Yes.

No, you learned that the tooth fairy doesn't exist

No.

Usually, the first thing to do when guessing about a random number from 1-100 is to split the possibilities in half by asking if it is more than 50 (or odd. Etc.)

The tooth fairy example gets a variety of responses, from people insisting it is just objectively wrong to say "the tooth fairy doesn't exist" to those saying it is just objectively wrong to say the tooth fairy was really my mother. I happen to agree with you about what the best way is to describe what went on in this specific case. However, this is a standard blegg-rube situation that is unusual only in that it is not clear which way is best to describe the phenomenon to others.

There is a constellation of phenomena that correlate to each other - the fairy being female, being magic, having diaphanous wings, collecting things for money, those things being stored under pillows, those things being teeth. None of these is qualitatively essential to be a tooth fairy to most people than "having ten fingers" is essential to being human. If tomorrow we learn that magic is real, a female sprite collects teeth from under pillows, and does so on the back of a termite (and has size-changing technology/magic, why not?), most people would naively say "the tooth fairy does not fly, but burrows on the back of a termite". That's OK, but not great if the true nature of the situation is not recognized, and they fall into error if they think "tooth fairy" has a meaning divorced from flight. Likewise, those who say "there was never a 'tooth fairy', there is rather the 'burrowing tooth fairy'" are right that there was never a thing exactly like the classic description, but this group makes an error if they demand the first stop calling the "burrowing tooth fairy" the "tooth fairy".

There is more to say, an individual who makes up explanations ad hoc is not communicating, and the relative confluence of idiolects is valid because of the tinkerbell effect. that makes saying "No, you learned that the tooth fairy doesn't exist" really peculiar, in the face of the many who hold the opposite position, likewise endorsed as language by common usage!

When it comes to "morality", the constellation of things represented with a token labeled "second order morality" had several stars, significantly organized around a few (mutually contradictory, but all validly denoted by the word "morality") sets of answers to these eight questions in the SEP on Moral Reasoning:

How do relevant considerations get taken up in moral reasoning? Is it essential to moral reasoning for the considerations it takes up to be crystallized into, or ranged under, principles? How do we sort out which moral considerations are most relevant? In what ways do motivational elements shape moral reasoning? What is the best way to model the kinds of conflicts among considerations that arise in moral reasoning? Does moral reasoning include learning from experience and changing one's mind? How can we reason, morally, with one another? What is the importance of institutional authority and social roles to the structure of moral reasoning?

One characteristic of things often (and validly) called "morality" is that they include the following among other pieces to answer the above questions: "'That which is good' is an ephemeral property that is infused in things in a dualistic way, it can be separate from all concerns beings may have, "good" can be binding in a way that is tautological and pointless...etc.

Reductionism continues the tradition of "morality", like other words, not meaning exactly what it did in the past, and it may be better to think of it as error theory in some cases. But all new theories claim the ones they supersede are in error, and there is nothing special about "morality minus magical deontology" or "moral reductionism" that one should consider them bad English by the usual standard.

After typing all of this, it strikes me that cars are a better example of no one component being essential. Cars without wheels will be "flying cars", unless they get sufficient lift and air etc. such that as one goes down the line of models from flying jalopy to sports flying car, each successive flying car will be called "car" by fewer and fewer people as it more resembles a fighter jet or so...as perhaps our descendants will call nuclear-powered flying vehicles.

The important thing is that reductionism gets it right when describing reality, the problems with deontology etc., and explains why people think erroneously, and it then proceeds to tell one how to act such that first order moral claims have meaning. If despite all that, you want to focus on its erosion of folk theories to call it an error theory, that is understandable, but it will be uninteresting if you say to the multitude "It is wrong(RC) to call reductionism 'moral'(RC)," since it is not wrong(everybody who recognizes not to misuse language by fixating on a connotation that often went along with a word when the contents described by that word are otherwise vindicated and under discussion, and we're discussing language which means 1) constelations and 2) tinkerbell).