Where does it say that one must provide a Jewish education for a child? Also, does it say anywhere that it is an aveira to NOT provide a Jewish education for a child?

Teaching a Jewish child Torah is an obligation included in the Torah commandment : "you shall teach them diligently to your children" (Deuteronomy= Devarim 6 6; see Sefer Ha Chinuch 419). There is a rabbinical obligation to train a Jewish child to the performance of mitzvot by having the child perform them and observe prohibitions even before he/she becomes an adult (Mishna Berura 343; Yoma 82a; Sukka 2b). These obligations are mandatory and self-evident; why should someone who recognizes the importance of Torah observance even consider not following them?