The problem is poor weight painting. The rig (since it’s Rigify) is working as intended.
There needs to be a better transition between the double bones of the forearm and the double bones of the upper arm.
Weight painting is only part of the equation to get good deformations. Having a model with good topology, is another. The edge flow of that mesh will not allow good deformations at the shoulders or upper arms with weight painting alone. It may require corrective shapekeys to correct the mesh.
Some of the bone placement for the rig is off a bit. (shoulders) This can also have a huge effect on deformations. In order to lift an arm above a T-Pose position, the shoulder must be rotated up or it will not look right. The shoulder also needs some better weighting.
I have a few tutorials on my youtube channel that cover weight painting for Rigify.
I am not saying that the topology is bad to be mean and I apologize if it sounds that way. I am trying to help show you where the model could be better for deformations and to reduce the amount of work needed to weight paint it. The upper arm has 46 vertices per edge loop and the leg has 40. I have rarely needed more than 12 verts per loop for a character with little muscle definition (for arms or legs) and maybe up to 16 with a higher res model. Reduce the overall vertex count of the mesh to simplify rigging and weighting. A subsurf modifier can be used to artificially increase the face count and to smooth the mesh.
Here is an example of a mesh with good loops defining the deltoids, clavicles, chest (pecs) and upper arms. (From MBLabs which is a free addon. http://www.manuelbastioni.com )