You ask your spouse for a divorce, and they tell you that they're not getting divorced. They don't believe in it. If you bring them divorce papers, they tell you they're not going to sign them. Then they look at you as if that decides it. Does it?
Not at all. Divorce is not something that takes two people. It takes one. As long as one spouse wants to end the marriage, they can divorce the other spouse with or without their permission. There is nothing your spouse can do to stop it. They are within their rights to ask you to reconsider or to suggest alternatives like counseling, of course, but they have no legal ability to stop you from doing what you want.
What if they still do refuse to sign even when you explain all of this to them? Most of the time, the court just rules that it's an uncontested divorce and grants it to you in their absence. This can take a short time, such as 30 days, to give your spouse a chance to respond to the filing. If they did respond, they may speed up the case. But after that time period is up, the court is just going to side with you.
In some senses, this could be a best-case scenario. If your spouse tries to ignore you, they can't fight you on any of the terms, and you're more likely to get an outcome that you approve of.
As you can see, in complicated cases like this, it really does pay to know your legal rights.