Responsibility is an important value to teach because no one can succeed in life if they are not responsible.
If students are not responsible, they will have trouble doing well in school. They will not take care to ensure that they get all of their assignments done on time. They will particularly have problems like this when they go away to college and do not have parents reminding them of what they need to do.
If people are not responsible, they may well end up in financial trouble. They may forget to pay bills when they come due. They may not think to invest and may, instead, spend freely without thinking of their futures. They may not take the time to think about what they can really afford and instead buy on impulse.
People need to be responsible so that they can be sure to do all the things that they need to do. Without responsibility, they will leave things undone and get in trouble. Therefore, this is an important value to teach children.