If Death Means Separation Between Body and Spirit, Then That Wouldn't Hurt Annihilationism At All

A common claim by annihilationists is that since the punishment of the unsaved is sometimes referred to as death, it helps annihilationism (since we know what dead bodies are like). Many (though not all) annihilationists are physicalists, or are dualists who believe in soul sleep, so to them, there is no conscious existence of any sort after death (until the resurrection when the body is made to be alive again). Since "death" describes the fate of the lost, you could see how this would be seen as supporting annihilationism. If they were clearly right about what death is, then we could leave it at that.

However, that is not a given. Also, since most traditionalists are dualists, it is worthy to note that, even if the immaterial soul does keep living on after death, the fact that the lost suffer "death"  still fits annihilationism better than it does the traditional view. This follow is an excerpt from "The Bible Teaches Annihilationism," from a section titled "The True Relationship Between Separation And Death":

Calvinists And (Most) Arminians Agree On More Than We Think - Part II

I. INTRODUCTION
Previously, we looked at how both Arminians and Calvinists believe in a sovereign God, despite the argument made by Calvinists to the contrary. Now, I want to look at it from the other side. Many Arminians claim that Calvinism falls apart when you take into account the passages that speak of God's desire to save all men. The reasoning goes that free will explains it perfectly, Calvinism cannot explain how God can desire the salvation of all when so many are not saved. However, there need not be any real disconnect. Both sides can hold to their view on election and still give reasonable and ultimately quite similar explanations for how God can desire the salvation of all without all being saved.