National holiday! Not listening to politicians as usual.
Let's consider the wider geopolitical context of the event, especially the other conflict going on in the Middle East: the Suez Crisis.

First the dates.
Hungarian revolution: 1956 October 23 to November 11
Suez Crisis: 1956 October 29 to November 7

Events in tl;dr format.
Hungarian revolution:
Due to the mismanagement and oppression a popular movement removed the Stalinist elite and made steps to reform the communism regime and leave the Eastern Block. The Soviet Union set up a new client regime which they installed with military intervention.
Suez Crisis:
Nasser of Egypt was kicking out the French and Brits from the Suez Canal, so they conspired with the Israelis to take it over. Israel invaded the Sinai and France with Britain pretended to intervene by separating Egyptian and Israeli forces so they can occupy the Canal. The US with the help of the SU and the UN told frogs and limeys: No! Then a UN force was formed to keep everyone out.