Why did parents oppose us participation in the war?

It depends on which war. Parents of fighting age children have often opposed their children going off to war, because they did not want their children to be killed. But this varies by region-- some studies have shown that southern parents are generally more supportive of their children engaging in military service. However, even when parents don't want their children to fight, there are exceptions. One example was World War II, where after the U.S. was attacked at Pearl Harbor, popular sentiment changed dramatically and nearly everyone (parents as well as young people) became a proponent of going overseas and defeating Hitler and his allies.