Sometimes, people don't want to be served. They may try to dodge a process server. They may refuse to sign the green certified mail card. Further, they may simply refuse to acknowledge the divorce petition and summons.
People do this for many reasons. Some are religious; some are nonsensical. Regardless of the reason, if your spouse dodges your service attempts, you have options.
Depending on the state where you live and where you're filing for divorce, you may be able to serve your spouse by mail, leave the divorce papers and summons at their door, or publish a notice in the paper. State rules vary, so make sure you get good advice about what you can and cannot do.