Irresponsibility is in the eye of the beholder. Chris is not irresponsible, but he conceives of being responsible in a way that his parents don't understand. Joe Keller, for instance, thinks Chris is irresponsible about money because everything has always been handed to him. Joe says to Kate about Chris,
You make a deal, overcharge two cents, and his hair falls out. He don't understand money. Too easy, it came too easy.
During the war, Chris moves beyond the narrow concept of responsibility his parents have. His parents are selfishly focused on being responsible only to themselves and their children. They don't have a sense of social responsibility. Chris does, especially as he watches his men care and sacrifice for each other during the war. He tries to explain to Ann,
Everything was being destroyed, see, but it seemed to me that one new thing was made. A kind of ... responsibility. Man for man.
What he means is that the soldiers seemed to be developing a stronger, broader, more unselfish form of responsibility in which they felt responsible for people beyond their own narrow circle of family. He believes that if people merely go back to living entirely for themselves and letting everyone else suffer, the war was pointless. What, he asks, was the good of so many people dying if a better world doesn't come out of that sacrifice?
As his parents intuit, this form of responsibility threatens them. They can't, for instance, be sure that Chris will not turn his father in to the authorities.