Something is wrong either at the cartridge wiring in the headshell, or possibly where the tonearm wires connect to the output sockets.I suspect that the Left and Right wires are wired in such a way to do as you describe. Double check that the cartridge is wired correctly, and no strands of wire are sticking out. Next, if you have a test meter, check that each wire has proper continuity by testing from the headshell end and at the output connector end. Make sure the red and white wires are the +, or center, of each output connector.If this doesn't find the problem, re-post and we'll think of something else.
Dave