For some, this is an issue of human liberty. For example, this rather conservative couple chose to draft their own marriage contract and were married outside of civil marriage:
http://ncrenegade.com/education/how-...out-a-license/
For others, civil marriage has consequences. Some who are currently unmarried qualify for medical insurance that helps them with rather serious medical bills, the cost of necessary medication, and procedures. When a couple gets a civil marriage, they are viewed by the government as a single civilly incorporated entity, and so their incomes and assets are combined. For many, this would cause them to no longer qualify for the medical insurance that they currently have and would essentially bankrupt them and have a serious impact on their overall health, and even shorten their lifespan.
Others have had civil marriages and have been through the terrible process of a divorce in the civil courts. They have experienced the injustice of a system that abides by civil laws that are unbiblical. Excessive attorney's fees, court costs, litigation, has often nearly bankrupted both men and women who were forced into a rather brutal divorce by a merciless spouse. When courts required legal grounds for divorce, civil marriage was truly something that offered security to couples. You see, when grounds for divorce needed to be established in a court of law, the guilty party was often penalized by being denied spousal support or child custody entirely or in part. The innocent party was also often compensated for emotional damage and the financial loss they would incur due to the divorce. But all of this changed when states abolished the need to establish grounds for a divorce and passed laws allowing for what is called, "no fault divorce". What "no fault divorce" means is that your spouse can choose to be unfaithful, or just choose to one day simply walk out on you after years of marriage... and they are automatically entitled to half of everything. If there is a difference of income and your spouse makes less than you, they are automatically entitled to spousal support. Some state laws also favor the mother with regards to child custody, even if she were the guilty party! And even more disturbing, some divorce courts are HOSTILE to Christian spouses. Many stories can be found wherein the civil courts essentially limited or denied custody to a Christian because their spouse brought up inflated charges of spiritual and psychological abuse from the Christian's religion or house of worship. With "no fault divorce" statutes in most states, civil marriage has ceased to offer the security it once offered, now it is truly a serious legal liability. Biblical marriage was supposed to provide security. And so civil marriage is unbiblical in this respect too.
It should be interesting to note that since the civil governments have passed laws allowing for "no fault" divorce, and statutes that cause divorce to be far more damaging to the innocent party, the number of couples who choose NOT to get a civil married before living together has increased, even among otherwise upstanding citizens. Fewer people want a civil marriage and for those who do enter into civil marriages, the numbers concerning divorce have increased.
For these reasons, among others, an increasing number of Christians are considering "covenant marriage" over "civil marriage". They do not want the GOVERNMENT controlling the terms and condition of their unions. They'd rather weather the outcome of separation privately, whatever it might be, than to have to have the court liquidate them and enforce unbiblical statutes upon their lives and finances. They want to take back control of their unions, their families, their finances, and their lives.
Remember, covenant marriages are not "illegal". There is no statute against performing them unless you're a licensed minister functioning as an agent of the state. There is no penalty under law for being in a covenant marriage. With powers of attorney, wills, and cohabitation agreements, a couple can secure the vast majority of rights a couple has in a civil marriage. However, control of these rights is in the hands of the couple, and not the government.
