An irreversible phase transformation (PT) from the rhombohedral phase of boron nitride rBN to cubic cBN was recently recorded at the surprisingly low pressure of 5.6 GPa at room temperature. In this paper, a very nontrivial and unexpected explanation of this phenomenon is found, based on our criterion for the PT in plastic materials and approximate solution of corresponding plastic problems. It is found that due to orientational plastic instability and rotational softening in rBN and the higher yield stress of cBN, stresses grow drastically in the transforming region during the PT (despite a volume decrease by a factor of 1.53). This allows the fulfillment of the PT criterion which takes into account the whole stress history during the transformation process. It appears that the above experimental phenomenon is connected to the mechanical behavior of the system of transforming particles+surrounding materials at the millimeter scale.