John 15:20

Jesus reminded the disciples of the principle that He had mentioned when washing their feet (John 13:16). Then He used this principle to encourage them to serve one another. Now He used it to explain why they would experience persecution.

People normally treat a person’s servants as they treat him. Since unbelievers persecuted Jesus, His disciples should expect persecution too. Conversely if some people in the world followed Jesus’ teachings, some would also follow His disciples’ teachings. This is a more likely interpretation than the one that sees Jesus saying that since they had rejected His teaching they would also reject the disciples’ teaching (e.g., NEB). Some in the world did indeed believe Jesus’ teachings, and some would believe the disciples’ teachings.