They do however teach that those who take Christ as their savior will be given eternal life. They twist the words of scripture to come to their conclusions. Look first at Matthew 25:46.
"And they will go away into eternal punishment, but the righteous will go into eternal life."
There are two words we need to focus on in that passage the first is “eternal” and the second is “punishment”. The word used in the Greek for “eternal” is aiónios which means eternal and unending. The same word is used for those who are righteous and “will go into eternal life”. Those who teach no “eternal” punishment must then concede that there is no “eternal” life. They can’t have it both ways.
Then we have the word “punishment”. The Greek word used there is kolasis which means chastisement, punishment or torment. There is no way they can make that word mean extinction or annihilation.
Paul, in 2 Thessalonians 1:9, uses a different word that they would have us believe supports their contention.
“Who shall be punished with everlasting destruction from the presence of the Lord, and from the glory of his power;”
In that verse the word used for “destruction” is olethros which is translated ruin, doom or destruction. Once again the word does NOT mean extinction or annihilation.
Where do unbelievers go after judgment? The same place Satan goes.
Matthew 25:41 Then shall he say also unto them on the left hand, Depart from me, ye cursed, into everlasting fire, prepared for the devil and his angels:
The Greek word used there for everlasting is aiónios and again the same word used for everlasting life. Satan and those who do not take Jesus as their Lord and Savior will end up in eternal torment. Those who trust in Jesus alone for their salvation will enjoy an eternal life of happiness, joy, and peace with Christ.
This brings up so many different things. I’ve got to address each one individually.
First, you said, “There are those who teach that hell, the place that the devil and those who do not accept Christ alone as their savior are destined for is simply a place where they are destroyed completely and will no longer exist. They teach that eternal doesn’t mean for ever and ever as we understand it.”
That is actually three things. First, hell: Hell is temporary and, in fact, thrown into the “lake of fire”. Second, “they” may not teach that eternal doesn’t mean forever and ever but I believe eternal means, frankly, permanent. So, when I see the bible say that something lasts forever and ever, that generally means “permanent” (though there are scriptures about when the bible said “forever” something was actually temporary or just a long time). But again, I interpret it to mean their “death” or “destruction” is permanent. It is not reversible.
Then you brought up Matthew 25:46. It is one of the verses I use as well. And as you say, one should consider what eternal punishment actually means. Regarding “eternal”, we are kind of in agreement. I think for the sake of argument that we can settle on “never ending”. Regarding the other word, one definition, as you pointed out, is “punishment”. Most people understand what that word means. Sitting in the corner is punishment. Prison time or the death penalty is also punishment. So, the wages of sin is death, and the punishment of death will be for eternity, never ending. It means you die and stay dead. Notice that I believe there IS eternal punishment as well as eternal life. There is no “both ways” about it. You and I merely disagree on what that punishment is, not regarding how long it lasts.
BTW, you mention that one meaning for punishment is “torment”. Well, throughout the bible, when God punished people, cities and civilizations, it was always very clear. They were not tormented. They were utterly destroyed and stayed that way. In some cases he made it clear that they would also be utterly forgotten – as if they never existed. Nowhere in the OT does God punish by anything resembling torture, UNLESS as a temporary sentence from which someone can return. i.e. torture punishment is used to teach a lesson to the one being tortured. The second death is not done to teach the lost a lesson. It is to remove them from the scene – like the chaff burned up.
Then you use Thess 1:9, to point out the meanings of the word “destruction” as ruin, doom or destruction. Yet you suggest that does not mean annihilation. OK. But I do know that if I destroy my house by burning it down, it has come to ruin and has been annihilated. We don’t want to over parse words here. Oh, and it’s ruin/destruction is permanent - also known as everlasting.
You then brought up Matt 25:41 regarding the everlasting fire and who it is prepared for. I think we have established that you and I agree on the meaning of the word “everlasting”. I also believe the fire will be everlasting. But how would a person have interpreted it on hearing Him say it. If I told you that I was going to throw your wife into an everlasting fire, would you not take that as a threat to kill your wife, rather than that she was going to suffer the pain of burning everlasting? Is the language not plain? Does it not mean that anyone suffering that fate has found their final condition, not to ever be reversed?
Meanwhile, as you say, “Those who trust in Jesus alone for their salvation will enjoy an eternal life of happiness, joy, and peace with Christ. “ On that we strongly agree.