John is the son of a priest, but that doesn't guarantee him the special training given to future priests. The text indicates that John has brothers, but none of them are training to be priests. John had to pass a test in order to begin training to be a priest. The test was simple. Be brave enough to hold on to a piece of metal and not die.
He looked at me with both eyes but I had not run away. He gave me the metal to hold—I took it and did not die. So he knew that I was truly his son and would be a priest in my time.
After that, John began receiving special training and treatment, because he would be a future priest.
Being a priest in training meant that John was held to a higher standard than other members of his tribe.
But when I boasted or wept without a reason, he punished me more strictly than my brothers.
There were benefits to being held to the higher standard though. John was allowed to sleep closer to the fire and was always given the best cuts of meat. This kind of treatment meant that John was more likely to be in top health.
Part of John's training allowed him to go to the Dead Places and learn about them and search for metal. John was also taught basic first aid techniques. He describes it as mystical healing, but it's clear that the training is basic first aid.
I was taught the chants and the spells—l was taught how to stop the running of blood from a wound and many secrets.
The last thing that John was taught to do is read. That skill's value doesn't become important until the very end of the story when John decides that he is going to help his people regain much of the knowledge that they lost before the Great Burning.