How can i tell if a person is the left or the right of the player?

Vector maths!

Taking player A's torsos as the origin, take the torsos of other players and see if the resulting CFrame/Vector3 is positive or negative on the x (which I assume is the left-right axis). After that, it's a matter of finding the closest player.

For e.g in a local script, this should get players on the left or right of a player.

local Players = game:GetService("Players")
local Player = Players.Player

RightPlayers = {}
LeftPlayers = {}

function PlayersOnRightLeft()
    for _, v in pairs(Players:GetChildren()) do
        local RelativePosition = v.Character.Torso.Position:vectorToObjectSpace(Player.Character.Torso.Position)
        if RelativePosition.X > 0 then
            table.insert(RightPlayers, v)
        elseif RelativePosition.X < 0
            table.insert(LeftPlayers, v)
        end
    end
end

This might not work as I have not tested it, but the idea behind it i.e the method you should be using is foolproof.