There are those who claim that reading does not help a child of three years old. In contrast, there are others who claim that a delay in reading can cause damage which is difficult to repair. Neither of these extremes is correct. It is impossible to build a child's education based on general theories. It must be accomplished by the facts on the ground.
We should not pressure a three year old to read, but it is not forbidden for him to read. Therefore, the educator who said that it is good to teach a three year old to read and write is correct, on the condition that it is a joyful experience for him.
This is indeed the guidance given by Rabbi Yitzchak Abarbanel, which is brought in the Shulchan Aruch (Yoreh Deah 255:5 in the Rama): we should begin to teach a three-year-old the letters of the Torah.
It is similar to a fruit: for the first three years it is Orla and forbidden to eat. Only at the beginning of the fourth year is the fruit for us (Biurei Ha-Gra ibid. in the name of the Tanchuma).
Nevertheless, we do not need to establish age requirements. It depends on the individual child and his will. Everything must be done with pleasantness, without pressure or tension. This will serve as the foundation for all of his future learning.