It's in our nature by birth. And that's not necessarily a bad thing in and of itself. However, it is incomplete.
The "perfect love" Jesus gives us (I John 4:15-21) can transcend these earthly reasons we have for loving others and open up new doors for relationships that our old nature would shudder to even imagine. "Narrow is the gate" (Matthew 7:13-14) that leads to a life of loving others without carnal motivation. I doubt any of us ever enter the fullness of this love expressed in our lifetimes, but the sanctification of the Spirit can bring us closer and closer to a love without barriers as we dwell in Him.
Sometimes we think we're there when we find a church. Instantly, you find a diverse group of people of (hopefully) many ages, races, economic backgrounds, and stages of spiritual and emotional growth. But even that may be a cover for an imperfect form of love as the common bond becomes the building, the mission, the identity, or whatever else the institution promises.
This under-developed, ulterior-motivated love can be compared to light filtered through a prism. For argument's sake, let's say the prism represents a church (or any institution, for that matter, be it a social club, the "regulars" at a restaurant, poker night crowd, etc.). The beam will represent someone's love.
When the light hits the pyramidal glass, it's dazzling and impressive. The concentrated beam of light breaks into the multiple colors of the spectrum. It's colorful, but it's diluted and each band of color is not as strong as the original beam. But it sure is bliss to bask in the colors.
The angle is off. And when the prism is removed, we see that the original beam of light was not directed at the same place where the rainbow once was, but somewhere else -- truthfully, the beam was only ever directed at the prism, not you.
If you're reading this, there's an almost certain chance you've been on the other side of this imperfect love before when you fall from the graces of the crowd you recently ran with. Whether you've once been rejected by a social clique in high school, fired from a job, benched for the season, or you happen to be on the wrong side of a local church schism, like the old saying goes "you find out who your friends are." It's tempting to write off those who stopped caring for you as soon as you left the group/team/whatever as phonies or (in the case of fellow believers) "fake Christians." To resist this temptation we must instead be moved with compassion for those who suddenly lost compassion for us.
We're not talking about understandable reasons for the loss of the closeness of a friendship: whether you move, change jobs, or a significant other pulls you in another direction, you don't frequent the same hangout spot or "third space" as much anymore, etc. These things happen, as close relationships wither with intentions of one day re-uniting. Paul's epistles are full of remembrances of his old friends, salutations to them (often by name -- see a long list in Romans 15), and his desire to one day reconnect with them.
Those persons who suddenly stopped caring as soon as you voted with your feet, strayed from the herd philosophically, or otherwise moved on? They have proven themselves to have imperfect love by their instant rejection. A better way to word that would be a love that has not yet matured. These persons need our prayers, not retaliation
As mentioned above, there are good reasons for a change in the closeness of a friendship, and there are also solid reasons for sudden dismissal -- relationships can be complex, and you have to chose your company carefully in order to hold on to a job or an intimate relationship. The Bible has a place for disfellowshipping others in extreme circumstances where sin may affect the entire Body. "Tough love" has a place, too.
What about you? Have you ever lost friends once the social "prism" was removed? Don't despair -- it's likely not a reflection on you, but a call to action to demonstrate "a more excellent way" (I Corinthians 12:31, and chapter 13), a more direct and meaningful love that only God can give.
UPDATE (6/5/17): Revisions made.