Perhaps another way of interpreting that statement is that you are responsible for not imposing yourself on other people. Assuming "other people" to mean any me

Perhaps another way of interpreting that statement is that you are responsible for not imposing yourself on other people. Assuming "other people" to mean any member of the human race, your interpretation would seem to mean "you are responsible for everyone you have any relationship with or to", which I don't think is what the parent commenter meant. Some are suggesting that responsibility for others is implied within a family relationship (spouses, children, elderly parents), but I disagree with this interpretation as it would exclude anyone without those relational ties from being recognized socially as an adult. I'm sure there are orphaned, spouse-less, childless people out there whom we would socially consider adults.