You're both correct, but his interpretation is a bit more common.
By definition: children of the first generation = second generation and children of the second generation= 3rd generation
But that's not the definition that many people use; when people say first generation, they mean the first generation that was 'generated' (ie born) in America. Immigrants aren't part of an American generation, they're part of some other country's generational history that arrived in America.
Usually when someone I meet says 'I'm second-generation (somewhere)-American' they turn out to mean their grandparents came from that place to the US and their parents were born here. I tend to meet more Asian- and Irish-Americans. Perhaps customs vary between different groups due to different traditions of counting? For example, a newborn baby is traditionally considered to be age 1, although most western countries would consider the baby's age to be zero (but some positive # of months).
By definition: children of the first generation = second generation and children of the second generation= 3rd generation
But that's not the definition that many people use; when people say first generation, they mean the first generation that was 'generated' (ie born) in America. Immigrants aren't part of an American generation, they're part of some other country's generational history that arrived in America.
Usually when someone I meet says 'I'm second-generation (somewhere)-American' they turn out to mean their grandparents came from that place to the US and their parents were born here. I tend to meet more Asian- and Irish-Americans. Perhaps customs vary between different groups due to different traditions of counting? For example, a newborn baby is traditionally considered to be age 1, although most western countries would consider the baby's age to be zero (but some positive # of months).