There are two sides to personal responsibility.
Personal responsibility has been a favorite catch-phrase of mine since I started teaching at my current school. It has helped me have higher expectations of my students and helped me be a better person. It is all about taking responsibility for one's actions and choices.
As a society, I think we've decreased in the amount of personal responsibility we expect people to take. We allow others to get away with excuses rather than demanding that they live up to requirements or their word. Think about how refreshing it is when someone accepts responsibility.
At the same time, I've come to realize that environment does impact an individual's ability to thrive. Perhaps this is best described as the difference between excuses and reasons.
It is important for individuals to take responsibility for their choices and actions. At the same time, it is our responsibility to cut people some slack in ways that are appropriate - to help the individual cope with their situation. This emphatically does not mean lowering our expectations.
For example, if I have a student who is having family trouble. I shouldn't accept sub-par work, nor should I allow the student to slack on turning work in. On the other hand, I can offer additional time in cases where it wasn't possible to complete the work for family-related reasons. Or offer additional help outside of class if the parents aren't there to offer guidance.
All things being equal, we should treat everyone the same. But of course, all things aren't equal. The trick is to help students develop their sense of personal responsibility while not simultaneously holding them responsible for things that aren't theirs. Maybe that goes for the adults in our lives, too.