All bones are part of one armature, both arms are one object as well. I did automatic weight thing and the mesh on the right arm acts as it should, but one on the left does that weird thing as you can see. Am i doing something wrong or?
Fist thing, the scale is -1 on the X axis, so apply the scale of your object:
Once done, you need to check the normals, enable Face Orientation in the Viewport Overlays panel:
Blue show face normal orientation, red the opposite, as you can see the normals are flipped outside on the right arm. To recalculate the normals, go in Edit mode, select all and press AltN: