This emphasis on learning came from two places: Jewish culture and upper class Roman culture. Both made sure that their children were educated as well as possible. Most early Christians were also Jews in the early years of the 1st century and they remained proportionately numerous until middle of the 2nd century, when their numbers declined drastically.** Their emphasis on literacy, particularly on knowing one’s own holy texts stuck around. By the 3rd and 4th centuries, many Christian converts, especially women, were drawn from the Roman upper classes. These were people who had been to a greater or lesser extent raised on philosophy and poetry. That they should teach their children and their fellow Christian converts was not a question.
Precisely what Christians should read and learn, however, remained a point of controversy. Was that non-Christian, non-Jewish philosophy and poetry worth learning from or not? Many felt that such works were unfit for Christian consumption, especially for women. Emilia, mother of St. Macrina the Younger made certain that her daughter studied none of these and learned reading and scholarship from Scripture and its commentators. St. Marcella agreed and she and her circle had a longstanding dispute on the topic with St. Melania the Younger and her followers, who agreed with Origen that such works should be studied and used to understand Christian texts better. Precisely how these women and their dependents were educated varied, but all of them saw its importance.
*More than possibly actually, but that’s not a debate I want to go into right now, especially since I have done nowhere near enough research for that.
**Largely due to the Jewish-Roman wars and the strong anti-Jewish sentiments of certain Gentile Christian leaders.
Life of St. Macrina - Tertullian.org
Life of Macrina - Internet History Sourcebooks Project
McNamara, Jo Ann. "Muffled Voices: the Lives of Consecrated Women in the Fourth Century." In Distant Echoes: Medieval Religious Women Volume I, edited by John A. Nichols and Lillian Thomas Shank, 11-29. Kalamazoo, MI: Cistercian Publications, 1984.
Pomeroy, Sarah B. Goddesses, Whores, Wives, and Slaves. New York: Schocken, 1995.