In past years my dad would fill his woodshed in the fall. We’d fill it with wood we cut the winter before; therefore the wood was pretty dry. We always had to clean the creosote out of the chimney a few times a year. Then one year he filled the woodshed in the spring, therefore the wood had all summer to dry (out of the rain). That winter, we didn’t have to clean the chimney even once. It made a very big difference to burn dry wood.
Not only does burning dry wood mean you don’t have the fuss of cleaning the chimney, but it is much safer because the chance of a chimney fire is much less.
There are more reasons to burn dry wood. It is certainly a lot easier to get dry wood to burn. They claim you get a lot more heat out of dry wood than you do out of wet wood because the dry wood burns much cleaner and you don’t lose as much energy in smoke. And you aren’t turning water into steam and losing it out the stack. That also means that burning dry wood is much better for the environment.
The only reasons I ever heard of for burning wet wood is you can hold a fire longer with wet wood. And obviously, if all you have is wet (green fresh) wood to burn, you’re better off burning wet wood than none at all.