The son of an investment banking executive has much greater opportunity to also become an investment banker than some rando dude from the street, even if it is remotely possible. That opportunity delta is real, and it's largely, almost entirely, due to family ties.
I would not say that I have the opportunity to become a billionaire, even though it is technically possible, but astronomically unlikely.
Immigrants don't have the opportunity to become president of the US because of US law, but any natural-born citizen of the country does have that opportunity regardless of the likelihood. The US has always had immigrants achieve boundless success here which is why it was considered the land of opportunity, not because everyone did - or because it was 'fair', but because it was possible.
> <Outcome> is somewhat inherited, therefore there cannot be real equality of <outcome>.
The US used to be a land of 'opportunity' for poor immigrants. They came to the US and worked hard to overcome their circumstances and make a better life for themselves and their children.
It would be insulting and demoralizing to them to say that opportunity is impossible because they're poor, because their uncle doesn't own the bank down the street. The point of opportunity is that it's _possible_ to succeed, the scales are not unfairly weighed against you by law or societal prejudice.
Many things make achieving outcomes hard - poverty, mental health, bad luck - these are sometimes affected by the past too, but they don't necessarily take away opportunity in that the hope in success is still possible. This hope is important to the soul is it not? This is why opportunity is so important, it's essentially hope.