Is teaching secular studies to one’s child required as part of the obligation of teaching a trade? Must a father send his son to college?
No. The father can decide to teach the child any trade that he can support himself with. Although many trades require prior secular education, the father is not obligated to teach his son specifically these types of trades.[1] Nevertheless, some aspects of secular education are certainly an obligation for the father to teach his child, as otherwise the child cannot enter into the work force. This would include teaching him the language of the country and perhaps mathematics and other secular subjects the child may need to survive in the workplace, or in a profession.[2] Being that learning these subjects is a Mitzvah, as it prepares the child for getting a job in the future, it is even permitted to learn these subjects in a Shul and Talmud Torah that is designated for Torah learning.
College: Many colleges teach matters of heresy and promote an environment that is contrary to Torah and Mitzvos, and hence it is forbidden to send one’s child there.[3] Nevertheless, it is certainly Mitzvah for the father to send his child to learn some kind of profession at a Kosher institution.[4] There is however no obligation to teach the child a sophisticated trade that takes many years to learn in [even a Kosher] college and university, and on the contrary, doing so is discouraged as it removes the person from his main job of learning Torah. It is possible learn a quick and easy trade and support oneself with it.[5]
[1] See Igros Moshe Y.D. 4:36
[2] Zera Emes Y.D. 107 p. 119a “Now that we are in exile, we must teach our children how to read and write the language of the country at a young age as otherwise they will be unable to get a job”; Shaareiy Rachamim 2 Y.D. 23 and Hod Yosef 1; Nachals Yisrael Sheiris Hanachala p. 10; Sefer Haitim p. 175 in name of Rav Haiy Gaon regarding teaching Arabic and math; Yabia Omer 7:21
[3] Mishneh Halachos 16:96
[4] Mishneh Halachos ibid
[5] Igros Moshe Y.D. 4:36 that it is possible learn a quick and easy trade and support oneself with it, and those who want to learn professions that take lots of preparation and study, such as a doctor or lawyer rather than learn in Yeshiva, are certainly following the advice of the Yetzer Hara.