System Information
Operating system: Windows-10-10.0.18362 64 Bits
Graphics card: GeForce RTX 2070/PCIe/SSE2 NVIDIA Corporation 4.5.0 NVIDIA 431.36

Blender Version
Broken: version: 2.81 (sub 16), branch: master, commit date: 2019-11-20 14:27, hash: rB26bd5ebd42e3
(Also happened in the newest 2.82 alpha from today (which also seems to have even worse combing performance))

Worked: (2.8 , 2.79)

Short description of error
The hair combing brush affects the hair on the opposing side of the mesh making combing impossible as already combed hair / fur gets ruined when the fur is combed on the opposing side of the mesh.

Exact steps for others to reproduce the error

Open the attached file for simple example of combed situation

or

Create new blend file and:

-Add hair particles to sphere or any other object, enable advanced mode (probably not necessary)
-Setup the fur so that there's enough parents like 1000 or so doesn't really matter but makes the error easier to see
-Go to combing mode
-You can make the fur symmetrical and enable mirroring if desired. issue happens in any case
-Comb something on one side of the mesh with the default combing brush
-Check the other side of the mesh opposing to the direction from where you combed (in viewport camera depth direction)
-Observe that the hair has also been combed on that side and depending on the camera angle / fov the area may be larger than the actual combed area was
-Try to make nice combing on the whole object and observe that combing gets ruined on the other side of the mesh as you try to get it done
-This error is also mirrored to both sides if mirror is enabled (not 100% sure)

Additionally selecting hair particles with C selection also selects the hairs on the opposing side and thus it cannot easily be used to limit the combing effect to some area

Depending on the mesh you can also see "live" how the error happens. When I comb hair around my animal character's eye looking towards the cheek of the opposing side, the fur moves on both cheeks even though I only work on the eye area because opposing cheek gets modified and them mirrored to both sides. This happens with mirroring enabled.

If these are caused by some "xray" system somewhere I couldn't find it and it shouldn't be on by default. And it wasn't on 2.8 as I already added fur to my character without issues but had to redo it and cannot get same results now due to this issue.