Matthew 10:34-39

Not peace, but a sword
v.34-36 Jesus says he came not to bring peace but rather a sword. Man against father, woman against mother. Christians will suffer persecutions from their own family. This was especially the case with Jewish Christians in the days this gospel is written. The Jews in those days expected the coming of the Messiah to be accompanied by peace and prosperity. Likewise in our day many in the church expect Jesus to bring peace (and/or prosperity). But we live in a world hostile to the true disciple of Jesus. There is untold suffering of Christians in the world today. See Lk 12:51-53 and Mi 7:6.
v.37 Jesus further explains that whoever loves father or mother (or son/daughter) more than him is not worthy of the kingdom. This is a hard teaching because we love our children. We must love our family and friends to be sure, but we must love Jesus supremely (Carson, Matthew).
v.38 We must follow Jesus in the face of possible rejection as when Jesus was rejected and carried his own cross. Mt 16:24 says we are to take up our cross and follow Jesus. Also Mk 8:34, Lk 9:23 and Lk 14:27. “Take up your cross” involves loving him and being willing to follow him no matter what the social or physical consequences.
v.39 As in Mt 16:25, Jesus here teaches that we find life (in the age to come) by losing our lives (perhaps disciplined self denial) for his sake. Here we are talking about discipleship and accepting or rejecting Jesus in this life has eternal consequences.

Read Matthew 10:34-39