But choice "B" clearly states that "both sides
..." I don't think that the sentence here portray "both sides" as a clubbed entity!!
In the context, between the use of ‘both sides’ and ‘each side’, I believe that ‘each side’ is to be preferred. Using ‘both sides’ may lead to the unintentional distortion in meaning that both sides are jointly planning something. A, B and E are out.
Between C and D, E is faulty for using ‘one another’, which I think is usable for a set of more than two, while the usage of 'for the other' in C is straight. C is the best.
We are twice armed if we fight with faith.
He who knows when he can fight & when He can't will be victorious.