What trade is the father obligated to teach his child?
The father is obligated to teach him a trade that will be able to support the common expenses in that country. The Gemara[1] states that the father is to teach him an easy and clean trade. A trade that is free of sin and of stealing, and does not involve the opposite gender. There is no obligation to teach the child a sophisticated trade that takes many years to learn, such as a doctor or lawyer, and on the contrary, doing so is discouraged as it removes the person from his main job of learning Torah.[2]
[1] Rebbe Meir in Kiddushin 82b
[2] 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.