During Jesus’ earthly time, some thought Him to be a peacemaker. He wasn’t; and didn’t intend to be. He made that so clear in Matt. 10: 34-39, in which He made the point that He had to be placed first and foremost in the lives of His followers, even if that meant creating a division among family members.
That seems rather harsh; something you wouldn’t expect a loving, godly person to say. But since I know Jesus to be the epitome of love, His statement must be seen as a help coming from an objective, spiritual point of view.
I see that view in John 3: 17-20. “For God did not send the Son into the world to judge the world, but the world might be saved through Him. He who believes in Him is not judged; he who does not believe has been judged already…For everyone who does evil hates the Light [Jesus], and does not come to the Light for fear that his deeds will be exposed.”
Jesus’ light and the earlier mentioned sword are the same. The sword is symbolic of the Word of God. And God’s Word, of course, is Truth. So the division that Jesus brings is the truth he speaks. For the truth, in and of itself, is divisive. Some will accept the truth; others will reject the truth.
As to why Jesus insists that He be placed above our relatives, it’s because it provides the opportunity for the unbeliever to be changed due to the proximity of the believer. That principle is discovered in 1 Cor.7: 14. There, it speaks of the believer as a blessing to the family; a holy, set aside opportunity for the unbelieving spouse or child.
If we as followers of Jesus don’t put Him first, then we are not worthy of eternal life, for Jesus is eternal life. If we don’t put Him first, then we will deprive Jesus of being lifted up before our loved ones so that He may have the opportunity to draw them to Him.
So though Jesus’ words in the Matthew passage sound harsh to the human ear, they ultimately are a spiritual reality that is a grace-filled offer of salvation.