Not necessary, because Larson has already been ruled out for an unavoidable scheduling conflict. It’s possible that he could also be ruled out due to lack of assertiveness; that doesn’t undermine the reasoning. The author never said “this is the only reason Larson can’t do the assignment.”

Necessary, because if the task CAN be assigned to someone other than a supervisor in the shipping department, then we have no reason to believe our options are constrained to Parker, Larson, and Franks.

Not necessary, because we’ve ruled out Franks due to lack of assertiveness. What would be true in an alternate world in which Franks does have assertiveness isn’t part of the reasoning. Perhaps the task would still go to Parker even if Franks could do the task.

Not necessary, because the issue with Larson is his “unavoidable” scheduling conflict. The author does need to assume that unavoidable scheduling conflicts prevent one from doing the task, but the author doesn’t have any opinion about avoidable scheduling conflicts.

Not necessary, because even if SOME people who are not supervisors in the shipping department have the assertiveness the task requires, the author believes that the task must go to a supervisor in the shipping department. This is why the author constrains the analysis to Parker, Larson and Franks. The author’s reasoning doesn’t extend to people outside of supervisors in the shipping department, so the author doesn’t have to have an opinion about those other people.