Is this fair to them? Definitely not.
Instead of ensuring certain comforts in old age, your parents made an investment into future. This way they get a peace of mind, a feeling of beating their own mortality, leaving something (well, someone) behind after they are gone. It's a great deal if that's how they see things.
Immigrants doing it in one generation, working blue collar jobs while sending their kids to the ivy league or med school, prove it's not based on real barriers either way.
It is extremely clear that our society, nowhere in the world, doesn't offer equality of opportunity; based on your birth, even accounting for genetics, your mid-life expected income could be predicted with decent accuracy.
It's great that you agree with me about barriers, but you might mention it to the posters in this discussion who are explicitly making claims of feudalism and apartheid. Beyond that, my post gave a logical explanation for probabilities. I don't see where you provided a counter to that logic, or even addressed what I said. How is my statement about three generations, for example, countered by your claim about predicting mid-life expected income for a single generation?
This is precisely the wrong model, one which accepts that there is no guarantee of equal opportunity. You're describing a promise almost as unworkable as the promise of heaven: if you're born poor, and you do everything well in life, your grandchildren's grandchildren will have a chance to enjoy the good life!
That is not what a democratic free society should mean.