I just don't understand why the armature on the left is deforming correctly, but the one of the left isn't. Why is this happening? What can I do to fix it?
Here's the blend file: https://pasteall.org/blend/cfa2bb7101fd41368a31e2141ac54982
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$\begingroup$ I don’t know why the one on the left is deforming correctly, but the one on the left isn’t, either. In fact, even if we were talking about the one on the right, the fact that there is one that works correctly does not tell us anything without examining the blend file, thus being a red herring detail that only makes the question seem more complicated. $\endgroup$– TheLabCatMay 18, 2022 at 22:56
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The meshes don't deform how you expect because their weights aren't right.
The better question is, why aren't their weights right?
Because you autoweighted meshes with backwards normals:
When they get autoweighted with backwards normals, the autoweight algorithm thinks, "Okay, whatever you do, don't weight the vertices to any bones that are outside of the mesh!" Like it should. And it uses your normals to determine what is the inside and the outside of the mesh. And it weights them to everything but the bone that you thought was inside them.
I saw that by enabling "face orientation" on the overlays dropdown. Everything blue has "properly" facing normals; everything red has backwards normals.
You can recalculate normals by selecting all of the inappropriate faces (or vertices) in edit mode and use a "recalculate normals" operation, ctrl n for me. When we do that, and then repeat our autoweights, we get deformation that is expected:
