Toph never told her parents the truth about Mr. Cheng.
Mr. Cheng would say things like, "The star that move too close to the sun catch alight and then it rains ashes. I call it stellar ash."
And Toph's parents say things like this: "You must become a strong young woman to support your future husband."
Mr. Cheng was her math tutor. She wasn't allowed to go to communal school with the other children her age, not even the other noble ones. She was blind, and therefore "helpless."
She was allowed during the day to take her math tutoring out into the garden. Mr. Cheng would tell her stories about the plants, like "This flower is called the peony, beloved flower of Avatar Salai. It is said to have sprouted on the very spot he shed a tear after his love was slain by a bandit. But enough rambling; have you finished that problem?"
And her father would say, "You are a child and I am your father. I will protect you."
Mr. Cheng would say, "You can be strong, despite your lack of eyesight. I have known many a strong individual who overcame similar maladies. The bard Zhurong was regarded as the greatest singer in all the land. But not many know he was born with acute asthma. Could exert himself for long before he was on the ground, gasping for air. But! He did not let that deter him. Legend says he traveled west through a storm that lasted a whole day and a whole night. On the morning of the third, he reached the Red River, where he asked for help from the gods. Lei Gong the Punisher took pity on him and cast a bolt of lightning at the river. As it caught fire, he heard a voice tell him to drink the fiery water. He did, and his lungs were healed. Now, I'm not saying drinking fire will cure your vision. He worked hard, and waited for his faith to help him."
Toph thought his stories were much better than her mother's.
"Toph, you mustn't venture out of these walls," she'd say. "Beyond them are Gudiao. Horrid horned birds with cries like a baby's and hunger for young children. You best stay away from them, lest they smell you."
When Toph asked her father about Gudiao, he simply said, "Those beasts are dangerous."
Mr. Cheng's hands moved when he spoke about the folklore of the world. They waved when was happy, shook when he fumed. He clapped them when he reasserted the topic toward mathematics after deviating. He clapped a lot.
The last time Toph saw Mr. Cheng was before leaving to help the Avatar.