According to the link you posted, the definition of "persecute" is
"to treat someone unfairly or cruelly over a long period of time because of their race, religion, or political beliefs or to annoy someone by refusing to leave them alone"
This may hurt the victim's feelings/emotions, but usually
"injure" is used to mean "to hurt or cause physical injury".
Coming back to "badger", it means "to persuade someone by telling them repeatedly to do something, or to question someone repeatedly".
While it may bother (annoy) the person, it is not the purpose
of the person doing the badgering. He/she is just after getting something
So, just as in badger:bother there is no direct intention of annoying,
I think in persecute:injure, there is no direct relation
in the sense that "persecution" is at a mental/emtional level,
but "injury" at a physical level.
I am not sure if this is the right explanation. I worked backwards
to come up with the explanation. Given limited time (as in exam
setting), I would have chosen B. :-p
Student or Learner