Background: Hildegard of Bingen (German: Hildegard von Bingen; Latin: Hildegardis Bingensis; 1098 - 17 September 1179), also known as Saint Hildegard and Sibyl of the Rhine, was a German Benedictine abbess, writer, composer, philosopher, Christian mystic, visionary, and polymath. She is considered to be the founder of scientific natural history in Germany. Hildegard was elected magistra by her fellow nuns in 1136; she founded the monasteries of Rupertsberg in 1150 and Eibingen in 1165. One of her works as a composer, the Ordo Virtutum, is an early example of liturgical drama and arguably the oldest surviving morality play.
Context: Maddocks claims that it is likely Hildegard learned simple Latin and the tenets of the Christian faith but was not instructed in the Seven Liberal Arts, which formed the basis of all education for the learned classes in the Middle Ages: the Trivium of grammar, dialectic, and rhetoric plus the Quadrivium of arithmetic, geometry, astronomy, and music. The correspondence she kept with the outside world, both spiritual and social, transcended the cloister as a space of spiritual confinement and served to document Hildegard's grand style and strict formatting of medieval letter writing. Contributing to Christian European rhetorical traditions, Hildegard "authorized herself as a theologian" through alternative rhetorical arts. Hildegard was creative in her interpretation of theology. She believed that her monastery should exclude novices who were not from the nobility because she did not want her community to be divided on the basis of social status. She also stated that "woman may be made from man, but no man can be made without a woman." Because of church limitation on public, discursive rhetoric, the medieval rhetorical arts included preaching, letter writing, poetry, and the encyclopedic tradition. Hildegard's participation in these arts speaks to her significance as a female rhetorician, transcending bans on women's social participation and interpretation of scripture. The acceptance of public preaching by a woman, even a well-connected abbess and acknowledged prophet, does not fit the stereotype of this time. Her preaching was not limited to the monasteries; she preached publicly in 1160 in Germany. (New York: Routledge, 2001, 9). She conducted four preaching tours throughout Germany, speaking to both clergy and laity in chapter houses and in public, mainly denouncing clerical corruption and calling for reform. Many abbots and abbesses asked her for prayers and opinions on various matters. She traveled widely during her four preaching tours. She had several fanatical followers, including Guibert of Gembloux, who wrote to her frequently and became her secretary after Volmar's death in 1173. Hildegard also influenced several monastic women, exchanging letters with Elisabeth of Schonau, a nearby visionary. Hildegard corresponded with popes such as Eugene III and Anastasius IV, statesmen such as Abbot Suger, German emperors such as Frederick I Barbarossa, and other notable figures such as Saint Bernard of Clairvaux, who advanced her work, at the behest of her abbot, Kuno, at the Synod of Trier in 1147 and 1148. Hildegard of Bingen's correspondence is an important component of her literary output.
Question: why not?
Answer: Because of church limitation on public,

Background: Simone Lucie Ernestine Marie Bertrand de Beauvoir ( or ; French pronunciation: [simon d@ bovwaR] ( listen); 9 January 1908 - 14 April 1986) was a French writer, intellectual, existentialist philosopher, political activist, feminist and social theorist. Though she did not consider herself a philosopher, she had a significant influence on both feminist existentialism and feminist theory. De Beauvoir wrote novels, essays, biographies, autobiography and monographs on philosophy, politics and social issues. She was known for her 1949 treatise The Second Sex, a detailed analysis of women's oppression and a foundational tract of contemporary feminism; and for her novels, including She Came to Stay and The Mandarins.
Context: De Beauvoir was intellectually precocious, fuelled by her father's encouragement; he reportedly would boast, "Simone thinks like a man!" Because of her family's straitened circumstances, de Beauvoir could no longer rely on her dowry, and like other middle-class girls of her age, her marriage opportunities were put at risk. De Beauvoir took this opportunity to do what she always wanted to do while also taking steps to earn a living for herself. After passing baccalaureate exams in mathematics and philosophy in 1925, she studied mathematics at the Institut Catholique de Paris and literature/languages at the Institut Sainte-Marie. She then studied philosophy at the Sorbonne and after completing her degree in 1928, she wrote her diplome d'etudes superieures (roughly equivalent to an MA thesis) on Leibniz for Leon Brunschvicg (the topic was "Le concept chez Leibniz" ["The Concept in Leibniz"]). De Beauvoir was only the ninth woman to have received a degree from the Sorbonne at the time, due to the fact that French women had only recently been allowed to join higher education. De Beauvoir first worked with Maurice Merleau-Ponty and Claude Levi-Strauss, when all three completed their practice teaching requirements at the same secondary school. Although not officially enrolled, she sat in on courses at the Ecole Normale Superieure in preparation for the agregation in philosophy, a highly competitive postgraduate examination which serves as a national ranking of students. It was while studying for the agregation that she met Ecole Normale students Jean-Paul Sartre, Paul Nizan, and Rene Maheu (who gave her the lasting nickname "Castor", or beaver). The jury for the agregation narrowly awarded Sartre first place instead of de Beauvoir, who placed second and, at age 21, was the youngest person ever to pass the exam. Writing of her youth in Memoirs of a Dutiful Daughter she said: "...my father's individualism and pagan ethical standards were in complete contrast to the rigidly moral conventionalism of my mother's teaching. This disequilibrium, which made my life a kind of endless disputation, is the main reason why I became an intellectual."
Question: Did she ever become a teacher with Merleau-Ponty and Levi- Strauss?
Answer:
Although not officially enrolled, she sat in on courses at the Ecole Normale Superieure in preparation for the agregation in philosophy,