I'm trying to loop cut on both arms symmetrically at the wrists so that they are equidistant from the chest. how can i do that automatically?
As said, the best way to model symmetrically is to use a mirror modifier, but that also means that you'll have all the model symmetrical...
If your model is not symmetrical overall, but you need to have some part modeled symmetrically, you can use an alternative approach, although there are limits to what you can do...
So, this could easily not fit to your needs, but hopefully it could give you just another idea:
here I "duplicated linked" the somewhat asymmetrical model, then I rotated it over Z 180° so to have one side aligned "to the other side".
Being a linked copy, the second object shares the same exact copy of the first object's mesh. But here it is somewhat "mirrored". And you see that the new edge loop positioning is replicated in real time (of course, it's the same mesh!).
Then on the first copy, I used loop cut on "one side", and placed the edge loop where needed. The same cut and position should be achieved o the other side...
To replicate the same cut on the other side, I activated snap tools (vertices), and after cutting, to create the needed geometry, I moved the new edge loop precisely to the position of the "other side" edge loop, using a suitable viewing angle.
It is just regular modeling, of course, but this gives you the chance to refer and snap to "the other side" of the same mesh (although "seen" through two different objects).
The mirror modifier has already been mentioned which is probably the best way but if you do not want to use that you can put a loop cut on each arm and then immediately pressing Esc so it stays in the middle. Then select both loops and scale by X so they move the same distance in both directions.