While didaskein normally takes an accusative or dative object, it easily can be tied to a genitive object by virtue of a conjunctive construction wherein the nearest infinitive to the genitive takes or can take a genitive object. The infinitive authentein may clearly take a genitive object, and the construction here just as certainly is a conjunctive construction, despite involving negation. The following notation from William D. Mounce, Greek professor and author of numerous works on Greek grammar, including his excellent commentary on Paul’s epistles to Timothy and Titus, provides additional insight on the syntax: William D. Mounce — "(b) Context and grammar allow andros, 'man,' to be the object of both didaskein, 'to teach,' and authentein, 'to exercise authority.' Moo notes, 'In Greek, objects and qualifiers of words which occur only with the second in a series must often be taken with the first also (cf. Acts 8:21)' (Trinity Journal 2  202). In this verse, the case of the object (andros in the genitive) is determined by the closer verb (authentein, not didaskein; cf. Smyth, Greek Grammar Section 1634). andros is not too far removed from didaskein for it to function as its object…). didaskein is moved forward in word order for emphasis, separating it from andros further than perhaps expected…" (Pastoral Epistles, p. 123).