Maybe if your parents can afford to pay thirteen thousand pounds fees a year - her school after all belongs to the private schools', Girls Day School Trust ( GDST) you will have the advantage of further financial help and connections after school and Uni, which belonging to a moneyed family may give you.
So she may be right for her audience.
For the rest of us who have no connections, no money to buy designer clothes for interview, no strings to pull, no parents who can pull in favours from friends, our certificates, our GCSEs etc. are all we've got to prove we are capable.
But she's not speaking to us and it would be highly irresponsible for a Head Teacher to speak so rashly to us.