Wilson did not want to stay neutral. He was trying to figure out a way to get the US into the war. But he appeared to stay neutral, only to get re-elected. He kept us out of war was his 1916 campaign slogan. But as soon as re-elected he did all he could to get us into the war. Franklin Roosevelt did the same thing, campaigning as if he kept us out of WW2, all the while planning to get us into the war. Lyndon Johnson did the same thing, campaigning as if we'd be in a war if Goldwater were elected. Then when LBJ won, he began to get us into the Vietnam War.
For Wilson though, he faced major isolationist sentiment. George Washington had warned us against foreign entanglements. John Quincy Adams warned against going abroad to find monsters to destroy. We had the Atlantic Ocean to keep us safe from foreign countries.
Memories still remained of the heavy casualties of the Civil War. We didn't want more dying. William Jennings Bryan resigned as Secretary of State in protest when he saw Wilson getting us into war.
There was suspicion of large corporations and large banks making money off war, at the expense of common people dying. Much like the WW2 comic strip "Orphan Annie" whose adopted father is "Big Daddy 'Warbucks'," as in making 'bucks', money off war. Michael Moore, whether right or wrong, made the same argument that we got into the Iraq war to get oil. There's a natural suspicion that those who make money off war are getting us into unnecessary wars.
The Germany of WW1 was not the Nazis of WW2. WW1 was no idealistic crusade, although Wilson claimed it was the "war to end all wars. Britain had ruled the world, with an empire, for centuries. Britain had been our arch enemy in two wars, 1776 and 1812. Helping Britain seemed out of place. We were the first and nearly only colony to escape its empire. It took war propaganda about supposedly brutal Germans to get us involved. Today's interventionist historians though tend to support Wilson's idealism and intervention throughout the world, ranking Wilson among the great presidents.
Wilson seized on the German sinking of a supposedly civilian passenger ship, although we had put military supplies on that ship, and it was a legitimate military target.
The Zimmerman note may have been the major factor. A German communication showed a possible Mexican German alliance should the US enter the war, with Germany promising to return southwestern US states to Mexico for its help. California, Arizona, New Mexico, Texas and parts of nearby states had once been part of Mexico. But Wilson would have seized on anything to get us involved. He had already invaded Mexico ostensibly to get Pancho Villa. Wilson seemed to like wars, and wanted more than his brief Mexican war got him. Historians seem to rank presidents as "great" if they preside over successful wars, such as Lincoln, FDR, Truman, Washington, Jackson, Polk and Wilson, as if they had much to do with how the military succeeded or failed, other than the two presidents who were generals.
Had we not intervened in WW1, France would have surrendered. Russia had already opted out of the war, after the Lenin revolution, leaving only Britain. France's "war hero' General Petain rallied his troops assuring his army that there would be no new offensive actions until Americans arrived. His French army had wholesale deserted or retreated, with no real hope of beating the Germans. Half deserted. Half ran to the rear, every time. We saved the day, but got little credit. General maxim: don't help people who won't be grateful or even recognize what you did for them. France never really returned the favor, to this day, as they sided with Saddam against the US in the Iraq war, and surrendered to Hitler faster than any surrender possibly in history, with "war hero" Petain collaborating with Hitler, becoming a war criminal. He's the guy we helped in WW1..