“ The Security Council, “ Considering that a grave situation has been created by the use of Soviet military forces to suppress the efforts of the Hungarian people to reassert their rights, “ Taking into account that because of a lack of unanimity among its permanent members the Security Council has been unable to exercise its primary responsibility for the maintenance of international peace and security, “Decides to call an emergency special session of the General Assembly, as provided in General Assembly resolution 377 A(V) of 3 November 1950, in order to make appropriate recommendations concerning the situation in Hungary.”
━ United Nations Security Council Resolution 120
Why couldn't the UNSC intervene or assist the Hungarian revolutionaries against the USSR forces? Only the Soviet Union voted against the Resolution, so what was stopping the UNSC from invoking Article 34 and following through with it?
The United Nations Security Council has five permanent members: the United States, the United Kingdom, France, China and Russia/USSR.
All have the power of veto, which enables any one of them to prevent the adoption of any "substantive" draft Council resolution, regardless of its level of international support.
So, why couldn't the Security Council pass a resolution to intervene in Hungary in 1956? Because the Soviet Union vetoed it.