Generations of boys from Cranbrook School in Sydney's east have endured rival private college students chanting a childish taunt across rugby fields and playgrounds.

'Get a girl, get a girl, get a girl if you can; if you can't get a girl, get a Cranbrook man,' goes one recent version of a decades-old rhyme.

The catchcry has changed slightly with the times but the slur always stays the same.

Pupils at Scots College further up Victoria Road at Bellevue Hill were once even known to mockingly doff their hats and offer a seat to Cranbrook boys on buses and trams. 

Now the all-male Anglican college and its mega-wealthy benefactors are embroiled in a schoolyard fight over whether the 104-year-old institution should become co-educational.

Billionaires are battling with other business and political heavyweights over whether boys and girls should mix as teenagers behind the school's wrought iron gates.

These parents are understandably passionate about their children's education. Annual fees at Cranbrook are up to $75,489 for a boarder and $39,894 for a day boy. 

The move to introduce girls at Cranbrook - at first in Years 11 and 12 - is supported by the country's third richest man, Scott Farquhar, the co-founder and CEO of Atlassian who is worth an estimated $26.41billion.

Farquhar and his wife Kim Jackson have offered to sponsor scholarships for girls coming from other schools to hasten the process.

Those against the move include former federal Labor minister turned political commentator Graham Richardson, famous for his personal motto 'whatever it takes'.

The conflict has led to accusations about a lack of transparency and featured sometimes fiery debate. It has not helped smooth concerns that the proposal was revealed not by the school itself but through a story in the Sydney Morning Herald. 

Evan Hughes, a Cranbrook old boy and son of the late art dealer Ray Hughes, referred to the school's unwanted old reputation in an opinion piece for the same newspaper. 

'Instantly the age-old joke popped into my mind: were they finally letting boys in?' Hughes wrote, before forcefully arguing for the proposed change.  

The plan to admit girls to Cranbrook was circulated by headmaster Nicholas Sampson among senior staff and school council members in April last year. 

It came amid an explosion of claims by young women of being being sexually exploited, assaulted and denigrated by students from all-boy private schools.  

The co-ed idea was met with early approval by many parents but immediately resisted by others who want to preserve the school's traditional identity.

Cranbrook has a junior campus at Rose Bay catering for kindergarten to Year 6 students. Some parents were furious the school would make such a fundamental change after they had committed their boys to 13 years of same-sex schooling. 

Cranbrook's most famous alumni are the late billionaire media mogul Kerry Packer and his son James, the Online Casino Web scripts Slots magnate who is selling his stake in Crown Resorts. 

Packer junior's longtime right-hand man Ben Tilley attended Cranbrook as did his onetime best friend and former Nine Network CEO David Gyngell. 

Others to walk its halls include businessmen Rodney Adler and Jodee Rich, who were both behind failed phone company OneTel, Packer's most spectacular early business mistake.  

Farquhar, who has children at Cranbrook, was the earliest high-profile supporter of making the school co-educational.

Other well-known parents have since emerged to let their stances become publicly known. 

Billionaire Gretel Packer, son of Kerry and brother of James, sent her two sons to Cranbrook and is among those who want girls at the school.  

Others backing the change include billionaire Caledonia chief investment officer Will Vicars and chair of venture capital firm OneVentures, Walter Lewin.