In the beginning, Bheeshma gave up his right to the kingdom. He decided not to get married so that he would not have any children to claim the kingdom. Having taken the stand that he would no longer be a ruler or king, he then became an ordinary citizen. Now, a citizen’s duty is to follow orders. He was an ordinary soldier and owed allegiance to that particular army, which were the Kauravas. He was beholden to the Kauravas.