Actually, it shows that quite a lot of integenerational mobility exists.
Consider this figure from the report showing the occupations of persons aged 30-44 in 2008 (my generation, just) compared to the occupation of their father when the child was 14 (mother where father not present). Except for managers and professionals, most children are in a different occupational category to their father.
Interpretation of ups and downs is more complex. Though using ABS occupational classifications, they have aggregated them in ways that are not properly explained. The way the figure is presented, it looks like ‘intermediate skilled workers’ are rated above ‘technicians and trade workers’, but using the ABS skills measure things are generally the other way around. There is a lot of subjectivity in these status measures.
But three-quarters of people whose fathers were employed in the least-skilled occupations are in a higher-skill occupation by age 30-44, and of those whose fathers were in professional or managerial occupations nearly half appear to have dropped to a less-skilled category (though in reality many technicians and trades people have higher skills and earnings than lower-level managers).
The education figures are also hard to interpret, not least because they suggest that HILDA (their source) is finding many more graduates aged 30-44 than the ABS. But the figure below suggests – consistent with the vast expansion of education over the decades – that there is considerable upward educational mobility across all parental backgrounds, except for those who cannot exceed their parents on these highly-aggregated measures (given the proliferation of postgraduate qualifications, this group is also likely to have significant upward mobility).
Undoubtedly, your parents matter. But there is plenty of movement up, down, and sideways.