I think the point was essentially that Greek and Latin as languages were only taught to the upper classes, those who pay for their education at private schools up to age 18. Those people, educated in subjects not open to the commoners, and at additional expense, then have an advantage when applying for a place an Oxford/Cambridge on the classics courses. Those courses then take in a disproportionate number of upper class students. Thus, the British class system is continued and reinforced by those universities that have been criticized in the past for not taking enough commoners.

Ie, they form a club based on talking dead languages no-one else understands and use Greek/Latin as a qualification for being included in the club, as well as where you were educated.

Class is very much a thing in the UK in certain circles. I have known people to succeed where others were forced to fail because of where they were educated.