Greig was born in Broughty Ferry, Scotland in 1880, one of eight children of textile merchant and higher education advocate Robert Greig, and his wife Jane.
From 1894 she attended the Presbyterian Ladies' College, Melbourne, but decided to leave school after 1896 and enrolled in an arts/law degree at the University of Melbourne in 1897, the first woman to enter the Faculty of Law, and indeed the first to enter any law school in Australia [REF].