The practice of social responsibility by state-owned enterprises is an inevitable requirement for promoting the high-quality development of the market economy and the healthy operation of enterprises. However, the traditional path of state-owned enterprises to practice social responsibilities is faced with practical predicaments such as unidentified practice subjects, uncertain practice rules, and unclear responsibilities. Through the analysis framework of altruism-egoism consistency, it can be seen that the inaccurate positioning of egoism, the confusion of social responsibilities among enterprises of different ownerships, and the failure to realize a dynamic balance of altruism-egoism behavior are the root causes of such predicaments faced by state-owned enterprises in practicing social responsibilities. Through theoretical and practical exploration, it is found that the Party organization in state-owned enterprises is the optimal choice for practicing social responsibilities. Hence, the rational path for the Party organizations in state-owned enterprises to fulfill social responsibilities should include the establishment of a “complementary relationship” between responsible entities, the clarification of “well-defined” practices, and the formulation of “scientific and reasonable” responsibilities, which also provides guidance for cultivating world-class enterprises with global competitiveness.