Agreed. However our parents did choose to have us, raise us, and give us the best fighting chance. Ignoring that ignores their hard work and skills to properly rear children. If in this new system we just give everyone a job and a good salary "because" then what incentivizes anyone to properly rear their children or give them anything other than the minimum the State mandates.
I'd argue that the drive to provide a better life for one's offspring is the fundamental building block of empathy. By society ignoring that capital that someone's parents built up in their children, you risk a change in behavior where parents say, "your life will be great because you will have a job and salary no matter what." Then, the very idea of love and empathy for one's offspring breaks down, and thereby in society as a whole.
Right, and we were lucky that they did so, which is my point. Plenty of people weren't so lucky, whether because of a lack of parents (e.g. orphans), neglectful/abusive parents, etc. Understanding that possibility is essential to understand why the playing fields aren't level.
"If in this new system"
I'm not proposing any kind of "new system", as I already explained. I'm just describing the problem.
"By society ignoring that capital"
I'm not calling for society to ignore that capital. If anything, I'm calling for society to recognize that not everyone has access to that capital by zero fault of their own and (ideally) to provide an alternative means to acquire equivalent capital. Folks shouldn't have to be punished for their ancestors' mistakes (or even non-mistakes).
A lot of this can and should happen through the public education system, but even that's not a given; even for those who have access to public education (which is far from 100%), not all public schools are created equal. It - again - more often than not boils down to luck.
I'm not really arguing in favor of anything. Just pointing out that personal success and well-being is indeed currently driven by luck, regardless of whether we like it or even realize it. Pretending that the only variable involved is merit or "hard work" is ignorant of the existence of billions of perfectly capable and "hard working" people currently unable to achieve such personal success due to circumstances entirely out of their control.
That problem is currently unsolvable (or at least very difficult to solve, and with no clear solution). I'm certainly not going to assume that I - of all people - have some kind of magical answer there.
It is, however, possible to at least gradually address the problem through whatever hard work it takes to make the next generation a little luckier: folks lending their shoulders for their children to stand on, and their children in turn lending their shoulders to their children, and so on. It sounds like your own ancestors did precisely that, as did mine. Whether we call it "luck" or "fortune" is a terminology issue that is irrelevant to the main point: the playing field is by no means level, and neither of us chose to be born into our respective families.