Is what I vowed – to teach my son Islamic knowledge and guide him to it – considered a vow, and is it permissible for me to teach him other sciences so that he may benefit Islam and Muslims, and what are the consequences for me if I am unable to fulfill this vow?

A vow (nadhr) is a Muslim's commitment to an act of obedience that was not previously obligatory for him. Therefore, vowing to teach a child Islamic religious knowledge is a vow that must be fulfilled. The vow follows the intention of its maker; if you intended to teach other sciences in addition to religious sciences, then you may do so. However, if you intended only religious knowledge, then it is not permissible to divert it from that purpose except for what its acquisition depends upon. If one is unable to fulfill the vow, then its expiation is the expiation for breaking an oath. What is required by the vow is merely guidance, and inability to fulfill it is unimaginable unless the son is lost.