I am assuming you have one of the older style washers that has the transmission rather than the newer ones with the sifter/shaft tube because the spin basket it rotating in one direction during agitation. But you will need to give your model number for us to be sure.
What I believe you have is a bad brake or bad brake bearing, which all this boils down to, is you will have to replace the transmission. Model example WBSR2080[T2]WW If the part of the model number I put in brackets is T1 –T8 then you have a brake bearing problem. You have to replace the transmission to repair this but the problem wasn’t the bearing itself it was the grease they used so if you took the brake bearing off and put new grease it may work again.
This page will help with replacing the transmission (or sifter if you have the new style). http://appliance-repair-it.com/GE-washer-disassembly.html