Do monks not have responsibility towards parents and family?

In this age, getting enlightened is not sought after by many as in Buddhas era. So I assume it must be harder for parents to accept such a decision. But monks who decide to ordain also have responsibility towards parents. How does that fit into ethics of Buddhas teachings? I understand giving Dhamma to parents is one of the greatest gift one can give to a parent. Can it not be done by living with them and still maintaining lay practice (like the potter who was an anagami and looked after his parents) Why ordain? NB: this is asked with due respect and do not wish to condone monks or people who desire to ordain. As Buddha would not have been a Buddha if he did not step out. I just want to understand ordaining in today's day and age.