I disagree. The closest connection Sloths have to Humans is (indeed) Eutheria.
Sorry about that. I need to proofread my posts better. I was trying to type "Epitheria."
But more importantly, I need to double-check my taxonomy, because Epitheria is wrong!
Sloths are in the clade Xenarthra, whose only other members are the armadillos and anteaters. This is an incredibly tiny group of placental mammals that is separated from the clade Epitheria, which includes
all other placental mammals!
In order for a sloth to be
less closely related to the primates, it would have to be a marsupial (or one of the other weird non-placental mammals like the egg-laying platypus). Raccoons, hamsters, rabbits, bats, manatees, shrews, elephants, giraffes and whales are all more closely related to us than sloths.
Sorry!
I've been carrying this idea around for a couple of decades: Sloths split off from shrews, and primates split off from sloths. That is certainly wrong. Perhaps without the benefit of DNA analysis biologists in those days had the relationships wrong. The grouping of families into higher-order taxonomic groups has certainly changed a lot; e.g., no one guessed that dolphins are closely related to cattle.
More likely, my memory has failed. After all, it's not "too big to fail."