The more I hear about it in class, the more it doesn't make sense to me. The Roman Catholic Church was meant to be a big symbol of good and the Vatican was the center of it, yet they did nothing? Can someone explain why they didn't pick a side?
hi! fyi, you can get started on this post from the FAQ's WWII section, which has an excellent response by /u/Domini_canes
Below, I am pasting in the response linked to by /u/Searocksandtrees in the interest of clarity. As always, followup questions from OP and others are encouraged.
First, you may be interested in an earlier post of mine in which I address the controversy surrounding Pius XII during WWII. It mainly deals with the accusations of silence regarding the holocaust, particularly from books such as Hitler's Pope.
As for your question specifically, the Vatican was required to observe neutrality in foreign affairs by the Lateran Concordat (or Lateran Accords), a bilateral treaty between the Vatican and Italy signed in 1929. Here is an English language translation of the treaty. Accordingly, the Vatican did remain neutral throughout the conflict.
This doesn't mean that the papacy was inactive during this time. Throughout the war, the Vatican communicated with all sides of the conflict and Catholics around the world. Along with many homilies and diplomatic statements, there was the annual Christmas address that garnered a good deal of international attention. These remarks focused on lamenting the continuing violence against noncombatants and repeated a desire for peace. In addition, the papacy issued seven encyclicals during the war. Encyclicals are letters from the pontiff to either a particular area or to the entire world. Of particular note are Summi Pontificatus (issued in October of 1939) and Mystici Corporis Christi (issued in June of 1943). Both links are to English translations.
As for actions, the Vatican was used as an intermediary between the belligerents. There are fairly reliable reports of German officers approaching the papacy to communicate their desire to throw a coup against Hitler to British officials. There are reports that are not confirmed to my liking that a German official warned the Vatican of the imminent roundup of Jews in Rome. One of the difficulties of this research is that the Vatican archives are not open for this period. The standard wait of 75 years before full access is granted has limited attempts to delve in any detail into the archives of correspondence for confirmation of the goings on of the Vatican. On a positive note, if you add 75 years to 1939 you get 2014, so it is expected that the Vatican will open up some of the documents for historians to get their hands on in the near future. (There have been some limited releases of documents, particularly in the Acts and Documents of the Holy See Relative to the Second World War. There are 'only' 11 volumes of these documents available at the current time)
On the diplomatic front, there were a number of Vatican initiatives. Gordon Thomas documents the Vatican attempts to shield Italian Jews from the Holocaust in The Pope's Jews. This included gaining visas and passports for targeted people. In addition, Pius XII tried repeatedly to get the US to cease or limit aerial bombardment. There were attempts to get the US to renounce the practice, to keep the bombers away from populated areas, and to keep the bombers away from Rome. Each attempt was completely unsuccessful.
As for assistance to either side, the papacy was accused of multiple occasions of favoring one side or another. Sometimes this was the case by both sides in reference to a single statement. The pontiff's calls for an end to aerial bombardment and to refrain from targeting civilians were often seen as unwelcome from the participating nations. Each wanted the papacy on their own side, and saw any criticism as aid or comfort to their enemies. In this author's opinion, the Vatican was in a nearly impossible position during the war. It was bound by treaty to observe neutrality in foreign affairs, and a great many Catholics had more allegiance to their nation than they did to their faith. As a result, calls to limit the horrors of war were ignored, as were calls for individuals to use their conscience to guide them to help those in need. With such limits in place, the Vatican was in a difficult position and was restricted in its efforts to alter the course of events.
As always, follow-up questions from OP or others are highly encouraged.