At what age is a father obligated to teach his child a trade?
There is no specific age recorded in the Poskim and hence seemingly so long as one continues to support his child there is no requirement to teach him a trade at an early age.[1] On the other hand he must teach him early enough so that when the child becomes independent he will now be able to support himself.[2] However, once the child is reaching of age that the parent desires or knows that he must support himself, then the father is obligated to teach him a trade. Practically, it is accustomed today [even in the secular world] to teach a child a trade only when he is older [of college age]. Thus, a person can go to Yeshiva throughout his teen years and when he is ready to get married and support himself the father is obligated to teach him a trade.
[1] See Kesubos 50a that in Usha they instituted to teach the child a trade after 12 years old. Seemingly this refers toa child that is incapable of Torah learning;
[2] There are also numerous Poskim who mention the allowance of teaching secular studies for children in a Talmud Torah as part of the fathers obligation of teaching him a trade. [See Sefer Haitim p. 175 in name of Rav Haiy Gaon regarding teaching Arabic and math; Yabia Omer 7:21]