Official Explanation
By pointing out the consequences of abandoning impartiality, the paragraph points out the importance for mediators of maintaining impartiality at all times. This is the point made in Choice B, which is therefore the correct answer.
Choice A is incorrect, because it goes further than anything asserted in the passage. The passage does not rule out the possibility that one can have an opinion about issues related to a dispute without taking sides in the actual dispute.
Choice C is incorrect because it is a presupposition on which the passage is based rather than the point of the passage; that is, the fact that the mediator is acceptable to both parties is a given, since they both ask the mediator to serve.
Choices D and E are both inconsistent with the main point of the passage, the importance of impartiality at all times, so both are incorrect.
Answer: B