But refuse - That is, refuse to pay attention to them, or reject them. Do not consider them of sufficient importance to occupy your time.
Profane - The word here used does not mean that the fables here referred to were blasphemous or impious in their character, but that they had not the character of true religion; 2 Timothy 2:16.And old wives’ - Old women’s stories; or such as old women held to be important. The word is used here, as it is often with us, in the sense of silly.
Fables - Fictions, or stories that were not founded on fact. The pagan religion abounded with fictions of this kind, and the Jewish teachers were also remarkable for the number of such fables which they had introduced into their system. It is probable that the apostle referred here particularly to the Jewish fables, and the counsel which he gives to Timothy is, to have nothing to do with them.
And exercise thyself rather unto godliness - Rather than attempt to understand those fables. Do not occupy your time and attention with them, but rather cultivate piety, and seek to become more holy.