Not saying that those situations are perfectly comparable at all, just trying to make a point that "if it was so good and easy, why isn't everyone successfully doing it" isn't really a solid argument for this.
Also, if it were true that people could be "self-made", we'd see a more diverse selection of "self-made" people. Instead, we see races and genders that aren't doing anywhere near as well as other races and genders.
If you think in terms of financial upbringing, we got a lot of diversity going. US has an insane turnover in terms of wealth, with a really high number of first gen millionaires and billionaires. Also note the fact that 70% of families losing wealth just a generation or two down the road[0]. Which is imo a very good thing, as it brings more evidence and support for the "self-made" theory.
In terms of social upbringing, just look at the numbers of top-tier CEOs and founders who are children of immigrants or immigrants themselves[1].
0. https://money.com/rich-families-lose-wealth/
1. https://www.cnbc.com/2018/05/30/us-tech-companies-founded-by...
Is there really such a thing as self-made? I honestly don't believe so. Otherwise, I think more people would do it.