Either ball joints or alignment come to mind.
Ball joints will often bind and grab in one direction but not necessarily in the other, when they are really bad.
You don't notice it jacked up because the control arms pivot down to put you on a different location on the ball joint.
You should be able to see which side and whether upper or lower, by seeing the pressure causing flex and jerks.
Although it is usually either one with a rubber rip or the lowers.
But alignment can do it also, especially of jacked up.
The camber or caster can be too great on one side, where turning the steering has to lift the whole truck up on one side more than the other, or it can strongly pull to one side.
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