I'm alse in the "greater-than-average" power in society. But I'd never say mine, nor yours, is an accident of birth.
Really?
I was born white. I was born middle-class. I was born in one of the largest cities in one of the world's richest countries. I was born to well-educated parents, who knew how to pass on their knowledge. I was born after certain civil rights movements gained significant advances for the position of women in society. I was born before No Child Left Behind and Proposition 13 gutted our school systems. I was born with better-than-average looks and much-better-than-average intelligence. I was in the right place at the right time to meet my husband. My kids happen to be attractive, smart, and neurotypical.
It is terribly frightening to those of us with good lives to think that, with a few small changes, we could have had bad ones. I can almost guarantee your sister didn't have "the same potential" as you. Undiagnosed mental disorders or learning disabilities? Trauma? Gender discrimination? Who knows. But your example of you and your sister proves my point: *you*, also, could have had a different outcome. The fact that you didn't doesn't qualify you to judge someone who did.
In college, I made a friend. A good friend. She and I are still best friends. For a while, after college, she lived on my couch. She told me, "If it weren't for you, I would be homeless." She's smart, educated, etc. etc. The primary difference between the homeless and "everyone else" is social support networks. Some people are good at creating those, and some people are not. Even those who are not may wind up with good families and/or friendships... or they might not.
Blaming the poor for being poor and the powerless for being powerless assuages our guilt in some way, but it doesn't even come close to the truth. The truth is, our individual wealth or position in society is *not* a reliable indicator of our internal worth as a human being.