I think to truly follow Christ, we have to be willing to let go of any and every (emotional) attachment to the world, including our attachments to loved ones. If we are focused on doing Christ’s work, then these things can hold us back, as they are levers for the enemy to use against us. Even our own attachment to our own life can be used as a lever to get us to do or say wrong things; to be truly focused on Christ we must not worry over these things.
That’s another way to describe it – to be so spiritually mature that you literally don’t worry about them. You can love them, but you have to be willing to let God handle their welfare if something happens to you.
Of course, if your vocation is raising a family, then it isn’t like you abandon the other people. It’s more like you know that everything in this world is temporal and lets you focus on the divine.
Alan