What problems did the US have remaining neutral when France and Britain went to war?
There were two problems that the United States had.
First, the two political parties in the US each liked one side (either France or Britain) and wanted to help it. The Federalists thought the French Revolution was a horrible thing and wanted to help Britain. The Democratic-Republicans hated monarchy and wanted to help France.
Second, both Britain and France kept interfering with US shipping. Each side would stop and take US ships that were trying to trade with the other side.
Both of these factors made it hard for the US to stay neutral.