Because
that’s what they really are… aardvarks are naked and sloths are hairy glyptodonts. And, yes, that comes as a surprise, it breaks a paradigm, it spins your head around, it’s heretical… and it’s exactly where the data takes us.

The Edentata is an odd clade
in which the basalmost taxa, like Barylambda, Glyptodon and Holmesina are very large. On the other hand, terminal extant and derived taxa, like Peltephilus and Cyclopes, are much smaller, just the opposite of most mammal clades (in which smaller usually lead to larger, following Cope’s Rule.)

According to Wikipedia,
“Glyptodontinae (glyptodonts or glyptodontines) are an extinct subfamily of large, heavily armored armadillos which developed in South America and spread to North America.”

In the large reptile tree (LRT, 1252 taxa) the glyptodont, Glyptodon, nests between the massive Barylambda and giant sloths, followed by smaller tree sloths and small extinct horned armadillos, like Peltephilus. On another branch (Fig. 1) another large glyptodont, Holmesina, nests between the massive Barylambda and the much smaller aardvark, Orycteropus, the armadillo, Dasypus, and the anteaters, Tamandua and Cyclopes.

Such a big-to-small phylogenetic pattern,
is known as phylogenetic miniaturization or the Lilliput Effect and is often the product of neotony (adults retaining juvenile traits, including juvenile size).

Figure 2. Holmesina, the glyptodont ancestor to aardvarks, anteaters and armadillos. Those are aardvark hands (Fig. 3), glyptodont feet.

Holmesina (Fig. 2) is added to the LRT today.
Basically it is a longer-snouted glyptodont, basal to the longer snouted above-mentioned aardvarks, armadillos and anteaters.

Following a reader comment,
(suggesting ‘taxon exclusion’ was the issue that did not unite glyptodonts with armadillos) I was looking for a transitional taxon to more closely nest glyptodonts with armadillos, rather than sloths. I did so and the tree topology did not change when Holmesina was added. Armadillos are still one taxon removed from glyptodonts, but at least now we have a glyptodont on the long-nosed clade of aardvarks, etc.. As before, aardvarks nest between glyptodonts and armadillos. Looking at all the edentate taxa in detail and overall. I think this nesting and this tree topology seem very reasonable (= it produces a gradual accumulation of derived traits at all nodes and between all taxa).

Figure 3. Orycterpus, the extant aardvark, is a living sister to Barylambda from the Paleocene. Aardvarks traditionally nest alone, but in the LRT they are edentates without armor… or hair.

Other workers, like Fernicola, Vizcaíno and Fariña 2008,
described the phylogeny of glyptodonts by putting taxa like Holmesina at the base while omitting Barylambda. Thus such studies do not present the full picture due to taxon exclusion. Everyone seems to omit Barylambda and all the other edentate outgroups back to Devonian tetrapods… but not the LRT.

Goodbye ‘Xenarthra’. Goodbye ‘Pilosa’. Goodbye ‘Cingulata’.
According to Wikipedia, “The order Pilosa is a group of placental mammals, extant today only in the Americas. It includes the anteaters and sloths, including the extinct ground sloths, which became extinct about 10,000 years ago.” According to Wikipedia, “Cingulata, part of the superorder Xenarthra, is an order of armored New World placental mammals.” In the LRT ‘Xenarthra’ (Cope 1889) is a junior synonym for ‘Pilosa’ (Flower 1883) and that is a junior synonym for Edentata (Darwin 1859).

References
Darwin C 1859. On the origin of species.
Fernicola JC, Vizcaíno SF and Fariña RA 2008. The evolution of armored xenarthrans and a phylogeny of the glyptodonts. Chapter 7 in: The Biology of the Xenarthra, Eds: Vizcaíno SF and Loughry WJ. University Press of Florida.
Gaudin TJ and Croft DA 2015. Paleogene Xenarthra and the evolution of South American mammals. Journal of Mammalogy 96 (4): 622–634. https://doi.org/10.1093/jmammal/gyv073

http://www.finedictionary.com/Edentata.html