Read: Matthew 8:19-20; Luke 9:57-62
And Jesus said to him, "Follow me, and leave the dead to bury their own dead." (Matthew 8:22 ESV)
Life and death. You are alive or you are dead. That's pretty much how we think. That is especially how the naturalistic kind of perspective trains you to think.
Really we are, all of us, born into death. The curse of sin that was brought into God's creation by His first created couple is something we are all faced with. And the only thing that rescues us from that curse is life in Christ.
The question of life or death is the question of Christ. To be in Christ is to be alive. To be outside of Christ is to be dead, even though you may still draw breath. This is to what Jesus was speaking of. He was drawing followers to himself that could be counted on guide Christianity in its infancy. Jesus was, and still is, looking for people who would be willing to walk from anything and everything the natural life had to offer in order to discover supernatural life in him. Where does that leave you?
I don't believe God is asking us to leave and reject our loved ones. He is however calling us to leave behind death and follow him into life. Life in Christ.