The initiating person may reluctantly agree to see if there's any way to save the marriage. Marriage counseling fails before it starts when the relationship is already over for the initiating person. It's only a last-ditch effort and lip service to appease the wounded spouse.
From a marriage counselor's perspective, there is no way to save a disintegrating relationship unless both people want to. There's no magic answer outside of the couple themselves. We can help clear communication, offer healing suggestions, help interpret what has happened and why, but we can't create motivation. Once it's truly over for one, it's over.
When divorce is inevitable, one partner can choose to proceed. Because of the availability of no-fault divorce, a person can obtain a divorce without the consent or cooperation of their spouse. The process will take longer because it can only go as fast as the slowest person. It's his or her divorce too. He or she must be able to eventually process the information and make decisions, but it will ultimately happen.
The initiating person will have to tolerate more frustration and likely have more expense because of the partner's resistance -- both in legal fees and in the settlement -- in order to exit the relationship. As was mentioned earlier, the initiating spouse thought about divorce long before the announcement. The non-initiator needs time to catch up -- to adjust to the coming emotional, logistical and financial upheaval. Minimally, two to three months are needed to accept the unwanted decision and come out of the initial emotional fog. For some, it takes much, much longer.
Unreasonable resistance, however, isn't wise because it's expensive. It will dissipate marital assets, leaving less to establish separate lives and for the children's education. Cognitive Behavioral psychotherapy is a good option for coming to terms with an unwanted divorce. Divorce Support groups are also very helpful. Both of these options help reduce the adjustment time and get a person onto a less painful, healthier and productive road to recovery.
It's wise to be sure the divorce is necessary, but if there's no hope for the marriage, letting go as gently and as quickly as possible will save the sanity and the assets of both partners and their children.