Because the Lusitania was sending weapons to Britain.
And Britain had a crippling Naval Blockade of Germany.
A true neutral would have told Britain that we would not risk our ships to aid them.
The Lusitania was a legal target but Britain helped push America into the war by sharing with America the Zimmerman Telegram.
The Zimmermann Telegram was a secret diplomatic communication issued from the German Foreign Office in January 1917 that proposed a military alliance between Germany and Mexico if the United States entered World War I against Germany. Mexico would recover Texas, Arizona, and New Mexico. The telegram was intercepted and decoded by British intelligence.
British revelation of the telegram's contents enraged Americans, especially after German Foreign Secretary Arthur Zimmermann publicly admitted on March 3 that the telegram was genuine. It helped to generate support for the American declaration of war on Germany in April.
https://historyofyesterday.com/the-zimmermann-telegram-d738d174b7f