“However, with regard to Torah learning, the Halachah is that if a father can afford one Rebbi, either for him or his son, if his son has potential to be a Talmid Chacham, he should give the Rebbi to his son, and forgo his own learning. Such an idea exists nowhere except regarding Torah learning.”
Which means to me that the father is required to work to pay tuition. After all, he is supposed to provide a teacher for his son’s potential (unknown as a child, so you should assume he could be a talmid chacham).