Humans are social creatures.
We have a base-level responsibility toward others, and always have ever since the first tribe was ever formed.
As society increased in complexity, cities and states formed and we began to raise armies, pay taxes, write laws, and abide by them or face the consequences.
Human history is a journey toward a more perfect understanding of how to get along with each other. When we’ve failed to live up to that idea, we’ve all suffered.
Social responsibility is an element of personal responsibility. It’s why you can’t rape any woman you see, murder those you disagree with, etc. etc.
Distill those dramatic examples down into the smaller, less-consequential decisions we’re faced with in everyday life and you’ll have the beginnings of how to live ethically.
“Personal responsibility” as used by conservatives seems to be offered as a get-out-of-jail-free card to avoid thinking socially or lifting a finger to help others. I do believe in personal responsibility, but I don’t only believe in it if it’s narrowly defined that way.