The fallacy: 'You go to a top university, everyone will be begging for you to work for them.'
Maybe up to 10 years ago, graduating with a first-class degree from a top-ranked institution would have been enough to guarantee a great job.
Source: https://www.hesa.ac.uk/news/16-01-2020/sb255-higher-education-student-statistics/qualifications#:~:text=The percentage of students achieving,class honours than male students.
However, when 28% (and rising) of students are receiving a first, and over 75% at least a 2:1, this is not sufficient to qualify for the most competitive roles. Your classmates will be competing for the same positions, and so will those at other institutions. The majority of these roles have acceptance rates of less than 1%.
Lets say McKinsey (top-ranked consulting firm) graduate recruitment receives 2 consulting applications:
The latter is far more likely to pass their gruelling CV screening process.
Now take a Cambridge Maths graduate with such a CV: