פירוש על קידושין 58:8

The Beraisa taught: to teach him Torah. From where do we know this? That it says in the Pasuk: That you should teach your sons. If someone was not taught by his father, he should teach himself, as the Pasuk says: and you should learn. How do I know the mother is not obligated to teach Torah?... Since the word “you shall teach” can also be written “you shall learn”: those who are required to learn torah are required to teach torah; those who are not required to learn are not required to teach. How do I know that she doesn't have an obligation to teach torah to herself? Since the word “you shall teach” can also be written “you shall learn”: those whom others are required to teach are required to teach themselves; those whom others are not required to teach are not required to teach themselves. A woman does not have to learn Torah because no one has to teach her. And where do we know this? Because it says in the Pasuk your sons, and not your daughters. The Rabbanan taught: If he can learn OR his son, he comes before his son. Rabbi Yehuda says:If your son is an interested person, smart, and has a good memory, then your son comes before you.

The Talmud provides a source obligating a father to teach his son Torah. And as with the other mitzvot, if the father does not teach the son, the son must learn himself.