Kaitoige introduces a concessive contrast: Jesus himself was not baptizing, although his disciples were.

As a conjunction, καίτοιγε introduces the qualification that Jesus himself was not baptizing while his disciples were, as the clause is presented in John 4:2.

1. Concessive qualification between clauses · dominant

   In John 4:2, καίτοιγε is tagged as a conjunction and introduces the clause qualifying the baptismal activity: Jesus himself was not baptizing, while his disciples were. The APB renders the verse, "although Jesus himself was not baptizing, but his disciples were."

   John 4:2

In the Anselm Project Bible: In John 4:2, the APB presents the concessive relation with "although,".