1. Carson says that "the verb authenteo in most instances has a neutral or positive overtone. But there is a handful of instances where you can at least make a case that it can have a negative overtone."
In fact, there are no cases near the NT in time, where authenteo has a positive overtone. I repeatedly asked John Starke to supply even one, but he declined to do so. ( I know he has a new baby, and I am very happy for him. However, he found time to make the clip of Carson on authenteo for CBMW.)
2. Köstenberger insists that both verbs must be either positive or negative.
Yes, most scholars agree with this.
3. All sides agree that "teach" by itself has a positive overtone.
I find this odd because Köstenberger on his blog has written the following,
- A case in point is I. H. Marshall. In his 1999 ICC commentary on the Pastorals, Marshall at the outset indicates his acceptance of the findings of my study by noting that it has “argued convincingly on the basis of a wide range of Gk. usage that the construction employed in this verse is one in which the writer expresses the same attitude (whether positive or negative) to both of the items joined together by oude.” Yet Marshall proceeds to opt for a negative connotation of both terms “teach” and “have authority,” because he says false teaching is implied in the reference to Adam and Eve in verse 14.