The heart of covenant is commitment to a person. It means favoring one person over another in a way that is perfectly acceptable and good. A father favors his own children over others' children in the investment of his time, attention, and resources. A husband likewise favors the relationship with his wife over other, secondary commitments.
This favoring is necessary because of the limitations of our humanity. As much as I would like to be there to support a close friend in a time of difficulty, he still takes second place if a serious situation arises with my wife. I am covenanted to my spouse in a way that I am not covenanted to my friend. Covenant says, come what may, this is the relationship that I refuse to put at risk. Or to put it in a crude sort of way, this is the person I will never throw under the bus.
But where human limitations are removed, so is the need to make these kinds of designations. I cannot be covenanted to all, but God is a different story. So part of what it means for God to establish covenant with each of us is the assurance that God will never put any of us in second place or risk His relationship to us.
Or, to put it more positively, each one of us enjoys the dignity of being the singular focus of God's favor. Not in a way that puts us in competition with each other, as though God would favor one of us at the expense of another. No, in God there is an endless supply of favor available - and He is delighted to invest His time, attention, and resources into each one of us!
"You're the One who never leaves the one behind."
Song: So Will I
The more we are conformed to His image, the more we too will live out of a covenant mentality with the people around us. Even if our actual covenants in this life are few, living from a covenant-based mentality means tapping into the brilliance and resources of God to increasingly favor all. It means having a heart disposition towards all to see them as family, as a "brother/sister for whom Christ died" (1 Corinthians 8:11), and to never have to throw anyone under the bus.