Divorce has become common and accepted in the world and in the church. The counsel given here we are not following to our hurt. First let's explore why the counsel was given.
Marriage according to Jesus was one man and one woman for life and the only reason to dissolve a marriage was unfaithfulness. Here Paul says divorce should never happen but if it does the one who demanded the divorce must either remain single or be reconciled. (Again I point out his first example is the wife seeking a divorce, a right not even available to a Jewish woman. The light of Jesus shining on the early church restored women to their rightful place of equality)
So the question is why does God not want a person who sought divorce getting remarried? I can assure you it is for our benefit not His. I always remind people that when you go to the doctor and he prescribes a course of action for you, be it a special diet or exercise or the cutting out of a bad habit it is for your own good not his and the only person who will suffer if you don't listen is you.
God's counsel is exactly the same. It is not some arbitrary punitive decree. It is counsel for our good.
Many years ago a man I knew decided he didn't want to be married to his wife any more and quickly was in a new relationship. Later he wanted to marry this new woman. I refused to be involved and he asked a pastor friend of mine to do it. I counseled him not to but he did it anyway. Today that man is divorced again. I knew from observation that the cause of the failure of the first marriage was primarily him. He lacked some of the basic skills necessary to live happily ever after. Changing wives was not going to change this reality. Statistics show that second marriages fail much more than first marriage and third marriages fail at a rate of 85%.
Think about it. The bond with our first spouse is the strongest. To break it and create a new one, it will never be as strong. God wants us to be happy. In Deuteronomy He said "Keep my laws that it may go well with you." Marriage is the most intense place for character development. If we do not learn the skills to coexist happily with another human being in our marriage, it is a delusion to think changing partners will fix everything. More often than not the one seeking the divorce is the primary cause of the unhappiness.