As early as 1834, an English lady, Mrs. Gutzlaff, wife of the Rev. Charles Gutzlaff, a missionary to China, came to Macao and, under the auspices of the Ladies' Association in London for the promotion of female education in India and the East, immediately took up the work of her mission by starting a girls' school for Chinese girls, which was soon followed by the opening of a school for boys also.

Yung Wing wanted the reader to understand that Mrs. Gutzlaff didn't know anything about educating boys.
Yung Wing wanted the reader to understand that Mrs. Gutzlaff was educating children in China for years.
Yung Wing included it to illustrate how common it was to have a Chinese child educated in English.
Yung Wing included the excerpt to explain how missionaries were the reason behind his education.