If any of you come to me without hating your own father, mother, spouse, children, brothers, sisters and even your own life, you cannot be my disciple. Luke 14:26
This sounds astonishingly harsh and actually inconsistent with the rest of biblical text, and I can understand that Jesus wants us to place the whole of our life in proper priority with Him as the head, the driving force of life. It's not that we lessen the value of relationships and life, but that we raise Christ and follow Him to an even greater status than all the rest. To elevate the value of Christ and Christ-likeness to a higher place comparatively to what we already hold dear is to esteem Him all the more. If we lessen significant relationships, we actually lessen the Christ position in us.
Greater love of earthly relationships should drive us to greater love of Jesus.
My example is in my relationship with my children. When I am in closeness with them, I think, "Lord, you love us more than this. You delight and desire my attention more than I do with them."
When the children are difficult or wayward, the same prayer thought comes, "You put up with us like this, too. We fail you, take paths away from your presence. Your heart is more broken than mine by this absence." It always leads me to my own repentance and desire to pursue Jesus.
Don't negate the vehicle of earth-bound relationships, but ride them to greater intimacy with Jesus.