Tell me, was Paul a Boomer as well?

Likewise urge the younger men to be sensible; in all things show yourself to be a model of good works, with purity in doctrine, dignified, sound in word which is irreproachable, so that the opponent will be put to shame, having nothing bad to say about us. (Titus 2:6-8)

It is one thing to address non-believing young men, another to address professed believers. I suppose a classical Christian school might not require a profession of faith, but most will, at least, assume it.  In any case, did Paul just miss getting to address the "Imago Dei masculine wiring" issues when writing to Titus...or Timothy...or to the church at Ephesus, or the church at Colossae, etc.?