One of the issues the Church (as in the whole body of Christ, not a specific denomination or church) has in modern Western culture is that we preach love, and the idea of love has been severely bent and twisted in the culture we live in. Love can run the gamut from sex and sexual attraction to a fleeting emotion that comes and goes by it's own will to, in many unfortunate cases, physical, emotional, or sexual abuse from someone. When a preacher or believer stands up and says God is love, the images that come to peoples minds are varied, and often do not match the intended vision, sometimes even if the listener is another Christian.
Our culture attaches the word love to a lot of things. So often in pop-culture, we see love as a motivation for sex. Songs, movies, and tv shows are wrapped in the idea that if we love someone, we take them to bed, or the backseat of the car, or wherever the "big moment" happens. Obviously, there is nothing sexual about God's love for us, but when dealing with things like God, sometimes the obvious must be stated. I have yet to see any evidence that the Greek word "eros", for sexual love, was ever used in any of the Bible's descriptions of God or Jesus' love, neither does there appear to be any use of the Hebrew word for lust in the Old Testament when referring to God's feelings towards His people.
Love is also seen nowadays as a high, a self-sustaining emotion, one that, should it fail to sustain itself, disappears. This attitude has created the proliferation of prenuptial agreements and do-it-yourself divorce kits. Fairy tales of happily ever after, mixed with again massive doses of romantic comedies and tear-jerker romantic dramas and cheesy love songs have created the idea that love just is, that once you are in love with someone, there is no effort required to remain in love. That idea, extrapolated out, tells people that if the feeling fades, rather than putting in the work to rekindle the flame, just to drop out. (Note: romantic movies and love songs are not inherently destroying our ideas of what love is, but when the fantasy is not balanced with some reality, we end up where we are at. Please don't write back that I told you you cannot watch :fill in your favorite romance movie/tv show here: that is not my point.)
Most people today have some experience, direct or indirect, with abusive relationships. Often we find that the victim in the relationship, and sometimes the abuser as well, really believe that the emotional, physical, or spiritual abuse in the relationship is really love. What goes through their mind when they hear that "God is love"?
1 Corinthians 13 is commonly known as the love chapter. It contains a long list of the attributes of love, and none of them match any of these modern definitions of love. " Love is patient, love is kind. It does not envy, it does not boast, it is not proud. It is not rude, it is not self-seeking, it is not easily angered, it keeps no record of wrongs. Love does not delight in evil but rejoices with the truth. It always protects, always trusts, always hopes, always perseveres. Love never fails" ( 1 Cor. 13:4-8 NIV) A pretty far cry from the first few paragraphs there, isn't it? Nothing about sex, nothing about butterflies in your stomach, nothing about love coming and going at will. Protection, trust, perseverance, patience, kindness, these are what love is, and this is the love that God has for us. His love protects us here, He trusts us with our free will, He is unbelievably patient with us. There is no need for a prenup, because as far as God is concerned, the love doesn't end. He loves us when we don't deserve it. Heck, God's greatest expression of His love for us happened 2000 years before anyone reading this showed up (John 3:16).
So what can the Church do? We have to keep taking the definition of love back. Say it loud, say it often, and when needed, use words. Say it from the pulpit, the street corner, the soup kitchen, the neighbor's kitchen, and everywhere else you go. These definitions didn't change overnight. These ideas didn't just spring up one day. It took time for the problems to proliferate, it's going to take time to repair the damage to society. But more importantly, just like love, it's going to take conscious action to keep the fire going.