Greasers originated from teenagers that lived in the northeastern and southern United States. A major part of this culture was the Rock and Roll music. Marlon Brando and James dean were two of the major influences of there style. The name "greasers" came from the hairstyle, brushing your hair back using hair gel or wax. They usually wear white or black t-shirt,black leather jacket and blue or black jeans.
Teenagers might have wanted to join a gang in 1960 because of the reputation,not just of one person but the as the whole gang. Also so they have respect and they could have had peer pressure. They could have had family issues, like being abused. Or even on what their living conditions were,like where they live. There might have been many gangs around the area.