…even so, the resemblance
clearly shows what pre-bats were like (Fig. 1), and not by convergence. Caluromys (right) is the last of the marsupials, transitional to basal placentals. Bats, like Pteropus (left), are not too far from basal placentals.
Figure 1. Pteropus and Caluromys compared in vivo and three views of their skulls. Note the hourglass-shaped nasals, similar frontals, similar overall silhouettes and similar palates. Juvenile Caluromys has only two molars, the same number found in all members of the Carnivora and by convergence Pteropus. Other basal placentals retain 4 or 4 molars.
Caluromys is in the ancestry of bats
in the large reptile tree (LRT, 1272 taxa). Caluromys shows where bats inherited their signature inverted posture, even though that genus is several nodes away from Pteropus.
Since Caluromys is basal to all other placentals,
maybe bats aren’t the odd ones after all, for hanging inverted. It’s the primitive way to go. All the other placentals that stopped hanging inverted are the derived ones.
We looked at the origin of bats
here and in earlier posts linked therein.
The Pterosaur Heresies 