Why were US citizens in favor of intervening in World War I?
I assume that this question refers to opinion in the United States before the US actually got involved in WWI. Once the US got involved, people would have been "for" the war simply because we tend to support our country when we are engaged in a war.
Before the US entered WWI, many Americans did not actually like the idea of getting into the war. Many Americans were of German descent and did not relish the idea of war with their ancestral country. Many Americans were of Irish descent and were not eager to help England in a war. Many other Americans simply felt that the war was not our business.
For people who did support the war, a major factor was German submarine warfare. The Germans used submarines to sink ships without warning, sometimes killing innocent passengers as happened when the Lusitania was torpedoed. People felt that this sort of warfare was barbaric. Some people also supported the war because they felt that the Germans were committing atrocities on the land, particularly in Belgium. Both the incidents in Belgium and the submarine warfare were played up by pro-Allied propaganda, which further helped drum up support for the war. This also helped people feel that the war was one which was being fought to protect international law and decency against an aggressive foe. Finally, many people supported the war because of our country’s ties with England. The US traded much more with England than with Germany, making us more likely to support England. We share a language with England and many Americans trace their ancestry to that country. All of these were reasons that helped cause some Americans to "be for" WWI before we became involved in the war.