Even sponges have 2 Hox genes

That would be (welcome) news to me.
AFAIK the current state of play is this:

The genome sequence of the sponge Amphimedon queenslandica shows that early metazoans possessed several Hox-like genes of the NK family, but Hox genes themselves arose and expanded only after sponges split from other metazoans.

source
primary corroboration

(Mycoplasma as variant placozoan?)

Unless there is a different Mycoplasma out there that I don’t know about, Mycoplasma are bacteria.

Do we know that the fungi arose from the choanoflagellates separately from the animals?

They did not. The choanoflagellates are more closely related to animals than they are to fungi.

And there are many single-celled animals

Actually, there aren’t. Some unicellular eukaryotes have been colloquially called “single-celled animals” but they are not animals.

Unless you count freshly fertilized zygotes.

Do we know that the fungi arose from the choanoflagellates separately from the animals? Has anyone suggested that fungi root among animals or vice versa? (Mycoplasma as variant placozoan?)

I don’t think any of us really disagree here, it’s just the rhetorical spin that bothered me.
Sure, multicellularity has evolved plenty of times, lots of other organisms have gametic meiosis and ingestive nutrition (and these are ancestral, not derived, traits in animals), and my take on the slime-mold abstract is that ‘epithelium’ evolved convergently (albeit with use of some homologous proteins) in animals and slime molds (to suggest that the common ancestor of Dictyostelium and animals actually possessed a multicellular epithelium to which both extant tissues are homologous strikes me as crazy-talk).

The criteria I listed were meant as a package, the Venn-diagram-intersection thing.

Some of them (still ) work on their own–collagen, for example–but ultimately the shared-derived characteristics that define/diagnose the clade are always going to be genetic.
So animals can be coherently defined as “all organisms sharing [this particular rRNA sequence]” or whatever, if nothing else.

implicit in your definition is the kind of phylogenetic statement I made

Actually, it was explicit (“the monophyletic lineage…”).

How about a phylogenetically explicit definition like “multicellular opisthokonts with collagen”?

Very interesting about gene-loss in extant choanoflagellates; I didn’t know that. Capsapspora is really not much closer to animals than mildew is, though, and it’s no “living fossil of our single celled ancestors” either; not by a long shot.

p.s. I did enjoy the piece and forwarded it to several colleagues.

I didn’t focus much on choanoflagellates because the latest work relevant to the article is mostly on Capsaspora. Choanoflagellates are indeed closer to us, but they also have undergone a lot of gene loss, so it’s not like the choanoflagellate genome is a living fossil of our single celled ancestors.

Anyway–thanks for the comment, and glad you liked the piece!

Animals cannot be defined, any more than your immediate family can be defined. The best that biologists could do for you is to say, “the animal kingdom is the common ancestor of all the living species we call animals, plus all their descendants.” There is no key to animals, there is no animalness.

I think that’s extreme. The monophyletic lineage we call ‘animals’ is distinguished by a few shared derived traits: multicellularity with cellular specialization (no, there are no unicellular animals except for maybe some obviously degenerate myxozoans, or is it mesozoans? I forget), a proteinaceous extracellular matrix containing collagen (a protein still unkown, afaik, in any other organisms), ingestive heterotrophy, gametic meiosis, a blastula stage of development, and then shared genetic traits such as similarity of rRNA, etc. These criteria include the sponges.

I thought the NYT piece was great, although it pretty much ignored the choanoflagellates, which are almost certainly closer to animals than, e.g., Capsapspora. We have a genome.

Motility would be another useful key to ‘animalness’, at least once we leave the level of microlife.

Any comprehensive definition of ‘animal’ would undoubtedly be a list of a number of elements, none of which would individually be exclusive to animals, but which would in their totality serve to separate animals from all other creatures. Envision a big Venn diagram, with a circle for each characteristic. At the intersection of all of these circles (sets) would be a definition of an animal.

I don’t claim to know enough biology to come up with a comprehensive definition of an animal myself, but your article would have been more useful to the general public had you at least attempted to more systematically identify some of the basic characteristics that make animals animals.

[CZ: Animals cannot be defined, any more than your immediate family can be defined. The best that biologists could do for you is to say, "the animal kingdom is the common ancestor of all the living species we call animals, plus all their descendants." There is no key to animals, there is no animalness. There are a 1200+ gene families found only in animals, but that's not a hard-and-fast definition--just a set of shared traits. What's more, it's likely that scientists will find new species of single-celled relatives of animals that will have some of those genes, too, taking those away from the "essence" of being an animal.]

More questions. Why is a sponge an organism and not a colony? It must have some sort of central organizer. What is it?

Guess I should read Carl’s books on biology.