If either of them were allowed to remarry it would have threatened the line of succession that Tiberius was comfortable with. By refusing Sejanus' request, Tiberius made it clear he was content with the children of Germanicus and his own grandchildren being his successors. Had Sejanus married Livilla, their children would have provided another line of possible successors. The implication of Agrippina's request was that she needed a man from outside the imperial family to serve as protector and step-father of possible imperial heirs, a powerful position. It was also an implied reprimand: Tiberius was meant to be the guardian of the imperial family.