First off, it is an inference question.
Second, the key part is just in the beginning, right there
A person who agrees to serve as a mediator between two warring factions at the request of both abandons by so agreeing the right to take sides later. To take sides at a later point would be to suggest that the earlier presumptive impartiality was a sham.
The rest of the sentence in its wording basically conveys the meaning: the person becomes biased or take a stance of one side or another and the result is a sham.
The inference at this point is pretty straight: we can conclude that the person BEFORE to accept the mandate should NOT become biased or have a tendency for one or the other side
B is the only that says this clearly
Hope this helps