Complete Apathy (3.5e Trait)
From D&D Wiki
You are incapable of emotions, and to other you may seem soulless
Prerequisite: No other traits or flaws related to emotions
Benefit: Any Sense Motive check against you take a -10 penalty, it is hard to discern when you are lying or telling the truth, as a result no one can ever fully believe you whether you're lying or not.
Drawback: Because of your inability to feel emotion your personality comes off rather creepy and to others you may seem as though you lack a soul. Therefore, you take -3 to all charisma based skill checks that involve interacting with others.
Normal: A character can freely show emotion, and in cases where someone may hide their emotions, they still feel them.
Roleplaying Ideas: You character could be possessed or under the control of an unknown force and your character acts as it's puppet. Your character could have had their emotions stolen by some evil spirit or demon, or maybe your character freely gave them up in exchange for something. Your character may have even lacked the ability to feel emotions from the beginning, such as in the case of an intelligent construct that never learned emotion, or is an outsider from a plane where no one can feel emotions.