Jesus is pretty blunt here.
[Do not suppose that I have come to bring peace to the Earth. I did not come to bring peace, but a sword. For I have come to turn a man against his father, a daughter against her mother, a daughter-in-law against her mother in law -- a man's enemies will be the members of his own household. Matthew 10:34-36]
Here Jesus is predicting more effects he will have on people:
[Brother will betray brother to death, and a father his child. Children will rebel against their parents and have them put to death. Matthew 10:21]
Here Jesus is advising his followers to abandon their families:
["I tell you the truth", Jesus said to them, "no one who has left home or wife or brothers or parents or children for the sake of the Kingdom of God will fail to receive many times as much in this age, and, in the age to come, eternal life". Luke 18:29-30]
Here Christ is literally telling his followers that good Christians should hate their families.
[Large crowds were traveling with Jesus, and turning to them he said: "If anyone comes to me and does not hate his father and mother, his wife and children, his brothers and sisters, - yes, even his own life he cannot be my disciple." Luke 14:25-27]
Here Christ is telling people they should avoid marriage if at all possible.
[...others have renounced marriage because of the Kingdom of Heaven. The one who can accept this should accept it. Matthew 19:12]
Here Christ is ordering a man to leave his dead father's body lying on the ground instead of burying him. Another man is told not to say goodbye to his family.
[But he said to him, 'Lord, let me first go and bury my father.' But he said to him, 'Leave the dead to bury their own dead; but as for you, go and proclaim the kingdom of God.' Another said, 'I will follow you, Lord; but let me first say farewell to those at my home.' Jesus said to him, 'No one who puts his hand to the plow and looks back is fit for the kingdom of God.' Luke 9:59-62]