This is completely untrue - if you google "effect of parents income on a child's education" you will find numerous academic studies which demonstrate there is a huge link between the educational attainment of the Father (and his income) and his children.
There's no denying some go on to good academic achievement and successful careers but the chances of doing so reduce significantly as the parent's educational attainment and income levels fall.
www.ons.gov.
uk/ons/dcp171766_378097.pdf
"Key points
• Previous research has shown that the UK has relatively low levels of intergenerational earnings
mobility compared with other OECD countries. By identifying the childhood factors that matter
the most to the intergenerational transmission of poverty and disadvantage observed in the UK, it
may be possible to gain a better understanding of the policies needed to improve income mobility
across generations.
•
Educational attainment has the largest impact on the likelihood of being in poverty and severely
materially deprived as an adult, both in the UK and the other EU countries studied. Holding all
else equal, in the UK, those with a low level of educational attainment are almost five times as
likely to be in poverty now and 11 times as likely to be severely materially deprived as those with
a high level of education.
• Growing up in a workless household also appears to have an impact on future poverty in the
UK.
Holding all else equal, those who lived in a workless household at age 14 are around 1.5
times as likely to be in poverty compared with those where one adult was working. However, this
specific effect of worklessness was identified as a significant factor in only one other EU country.
•
An individual’s assessment of their childhood household financial situation is not a significant
predictor of poverty and material deprivation in the UK once educational attainment is accounted
for. This suggests that household income during childhood mainly impacts future life chances
through the educational attainment of the child. However, these factors remain significant
predictors of poverty and severe material deprivation in the Southern and Eastern European
countries, even after controlling for educational attainment.
•
The father’s level of education has the largest impact on the likelihood of low educational
attainment in the UK out of the factors examined. Holding all else equal, people are 7.5 times
more likely to have a low educational outcome themselves if their father had a low level of
education, compared with having a highly educated father. Parental education level also has
the largest effect on the likelihood of low educational attainment across the other EU countries,
though the extent of this transmission varies and is highest for the Southern European countries,
as well as some Eastern European countries and Baltic States.
• In the UK, there is also a relationship between people’s educational outcomes and their mother’s
educational level, the number of adults and children living in the household, the employment
status of the parents and the childhood household’s financial situation"