When we define the term 'government' in syntax, we should exclude the interfering nodes which asymmetically c-command node B.Why can't we allow asymmetrical c-command while we accept symmetrical c-command? In other words, why should we allow the interfering nodes which symmetrically c-command B? Please let me know, please. :)
I have troubles parsing the question unambiguously. My answer assumes the question means "Why are symmetrical c-commanding nodes not barriers to government whereas asymmetrically c-commanding nodes are (potentially) barriers to government?" but I encourage you to rewrite the question with more details in case I misunderstood.
Under this assumption, the historically accurate answer was that this was a pure stipulation based on the fact that such an ad hoc fix gets the case assignment and binding properties right. The main problem with allowing symmetrical c-commanding nodes as barriers is the inherent ambiguity this involves: since binary trees have no ordering (so that their common drawing is deceptive), it would be impossible to define which node is a barrier for the other in the generic situation were symmetric c-commanding nodes to be allowed.
However, such stipulations should always be regarded with great skepticism and accordingly a good deal of works in that branch of syntax in the last 30 years has been devoted to eliminate them (the impetus behind the so-called minimalist program). Within the framework of minimalist syntax, the answer to your question follows from the data structure of the syntactic objects constructed by Merge, as I encourage you to work out for yourself (or ask about).