In these passages Jesus tells His disciples that ‘Jesus is the vine and they are the branches.’ Jesus said that one must bear fruit in their lives to prove that they are followers of Jesus.
Mere intellectual assent that Jesus is the Son of God is not enough. We must obey the Word of God in our daily lives, and in so doing we will bear fruit.
Jesus also said that the world will hate those who believe in and follow Jesus. The world hated Jesus. It will hate his followers, too. This fact makes it more difficult to follow Jesus, because we do not want to be hated or ridiculed by others, including family members.
However, we must have Faith that Jesus is the only way to Salvation. We must have courage to obey the Word of God when the world tells us otherwise. In fact, we must be ready to die for our Faith in Jesus Christ. Someday we may be faced with that situation. The Bible says that God will provide us the strength to do so. Praise God!