Okay, I'm clearly missing something here. So I can get heaven, hell, and this third choice where my soul becomes nothing?
You are clearly missing something.
Man has only two choices set before him: life or death.
Man is a mortal soul. All mortal souls die. You, me, Jesus, everyone who has lived and will ever live will die. It is appointed once for man to die. There is nothing man can do to change that. There is no escape from it. No man can choose not to die. Mortality always ends in death.
The choice man has is between life -> the life of age to come (immortality) and death -> the second death (annihilation).
Immortal souls aren’t subject to death -> they aren’t subject to the first death; they aren’t subject to the second death. In other words, an immortal person simply cannot die.
God alone inherently possesses immortality. God alone cannot die. God will never die. He is immortal.
The creator cannot die. The created, without exception, will die. But that isn’t the end of man’s story.
Man can become immortal.
You haven’t expressed any interest that I’m aware of in becoming immortal. The people you’ve been speaking with believe that you and they (as well as all other human beings) were born with an immortal soul. You weren’t, and neither were they or anyone else. All they‘ve done with their talk is place Platonic ideas in your head and confuse you. My advice: Listen to Jesus, not Plato.
If it were true that man inherently is, or has, an immortal soul, then man cannot die. (It was the devil, in the Garden of Eden, who lied when he said: “You will not die.”) Look around you. You know for a fact that man dies. It happens every day - approximately 150,000 times every day, worldwide.
Unlike mortal life, which every man has, immortal life is a gift from God, and not everyone will receive it.
Jesus’ teaching and preaching is all about God’s immortality plan for man.
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Heaven? No one goes there when they die. Even Jesus didn’t go there when he died. He was in the grave, the tomb, for three days and three nights. He went to heaven 40 days after he was bodily resurrected from the grave. He was mortal before he died. He was raised from the grave immortal.
Hell, that is, the grave? Everyone goes there when they die. No man can avoid it. There is no activity in the grave. The dead are lifeless.
Bodily resurrection? Everyone who has died will eventually be bodily resurrected from the grave - some, those who belong to Jesus, when Jesus returns, to inherit immortal life; everyone else will be raised briefly to mortal life a thousand years later, in order to be judged by Jesus, based on what they did in life.
Hell, that is, the lake of fire? This is not the grave. It is the place where punishment is administered to the incorrigibly wicked. The punishment for them is the second death, not immortal life. The punished are consumed in the fire; reduced to smoke and ashes. They will be annihilated; permanently ceasing to exist.