Our souls are not immortal at this point. The bible says, "To God who ALONE is immortal, be glory and honor..."
But when Christ comes into his Kingdom, "This mortal shall put on immortality."
The snake was the first to convince humanity that they were immortal. "You shall not surely die"
Then Father discusses with the Son that they needed to get Adam out of the Garden before he ate of the tree of life and would thus, "live forever" in a sinful state.
As many ET pastors say incorrectly (and indirectly saying we are all immortal), "It's not a question of whether you will live forever. Everyone will live forever, it's just a question of will you spend it in heaven with God or in hell (being tortured) for all eternity."