Hoist by one's own petard of "logic"

This widely-retold story is so classic, it's probably spurious. Nonetheless, it’s a good example of quod erat demonstrandum (QED) logic:

 A Republican state convention delegate speaks with a Utah GOP elected officeholder about immigration. The delegate argues that a fence should be constructed to span the entire USA-Mexican border to keep out illegal immigrants.
 GOP OFFICIAL: What happens when they climb the fence?
 DELEGATE: You electrify it. Then they won't touch it.
 GOP OFFICIAL: But what if they touch it? You would let them die?
 DELEGATE: It would be their choice.
 GOP OFFICIAL: What about a mother with a baby strapped to her back? You would let the mother and the baby die?
 DELEGATE: It would be the mother's choice to kill that baby.
 GOP OFFICIAL: Then you're in favor of abortion?
 [Silence.]