My colleague Justin Petersen wrote a blog post on "What It Takes to Be A Voice Teacher," which reminded me of Salvatore Marchesi's words on the matter, Marchesi being a student of Francesco Lamperti and Manuel García, and husband to Mathilde Marchesi, who was a highly successful teacher in her own right.
The human voice, being a physical instrument, is not only liable to millions of exceptional modifications resulting from the different peculiarities of every single organism, but to the climactic influence, to bad habits, and to physical disorders, which can alter its natural characteristics. Therefore, whatever may be the degree of the teacher's theoretical knowledge, he will never compass an important and continuously satisfactory result, if he lack the three indispensable qualities that act as guides for the human intellect; namely, instinctive intuition, penetrating reflection, and long experience. The teacher may utilize all the precious discoveries made by modern science, but on the condition that he understands them, and provided he knows where, when, and how they are to be employed.
Salvatore Marchesi, A Vademcum for Singing-Teachers and Pupils (1902): 7.