I don't want to get too deep into the linguistic arguments others have made, starting with how they come from Aion which means Age (Eon comes from Aion), which makes the use of it's Hebrew equivalent Olam in Daniel 12 the same issue.
That same Hebrew word for Eternal/Everlasting/Perpetual is used to describe how long the Aaron Priesthood will last (Exodus 29:9, 40:13-15, Numbers 25:10-13). But we know from the book of Hebrews that the Aaronic Priesthood had now been done away with and replaced with Jesus, Priest-King after the order of Melchizedek.
A better Hebrew word for Eternal would be Qedem (Strong number 6924) used of God in Deuteronomy 33:27. and Habakkuk 1:12.
No, the point today is to use Scripture to interpret Scripture, to show two places, two confirming witnesses, where Scripture uses this word in a way that in context totally contradicts it meaning eternal. Naturally these verses aren't the occurrences of the word used to build the doctrine of Eternal punishment.
Romans 16:25 in the KJV.
Now to him that is of power to stablish you according to my gospel, and the preaching of Jesus Christ, according to the revelation of the mystery, which was kept secret since the world began,In the Greek the last two words are Aionion and a word that means "kept secret". Aionion is translated "since the world began". There are other places where Aion is translated world rather then Age, like "My Kingdom is not of this World", and Paul calling Satan the "God of this World", it should be Age not World there as we know in the future Jesus will take ruler-ship of the Kosmos from Satan. The very next verse says "but now is made manifest". Proving that it can refer to a time period that will expire.
The other key verse is Jude verse 7.
Even as Sodom and Gomorrha, and the cities about them in like manner, giving themselves over to fornication, and going after strange flesh, are set forth for an example, suffering the vengeance of eternal fire."Eternal fire" there is Aioniou fire. There it is used in the exact same form it is in Mark 3:29, John 6:68, Hebrews 6:2, and Romans 16:26 referring to the "Everlasting God".
Obviously the fire that destroyed Sodom and Gomorrah isn't still raging north of the Dead Sea.
But also important is that Ezekiel 16:53 says that Sodom will be restored just as Samaria and Jerusalem are promised to be restored. Sodom had no survivors, they considered Lot a foreigner living among them even on their last day, and Lot's descendants became their own nations, Moab and Amon. And no one was a believer who perished in Sodom's destruction. Sodom can only be restored if eventually Jesus shed Blood redeems even the Sodomites.
In Revelation 22, those who were cast into the Lake of Fire are now just outside New Jerusalem.
And in in the Sheeps and Goats Judgment of Matthew 25, people overlook that neither the Sheeps or Goats were those who believed in Jesus in this life. We are the brethren. Chuck Missler likes to say they are the Jews here (and argue this isn't the same judgment as the White Throne judgment). But earlier in Matthew Jesus had effectively disowned His mother, brothers and sisters and said His real Brethren are those who believe in Him.
Luke 3:6 says that all mankind will see God's Salvation. Romans 5:18-19 says that as by one Man's Sin all are condemned, so by one Man's righteousness all men are Justified. Romans 11:32 says all Men are bound to Disobedience so that he might have Mercy on ALL men. 1 Corinthians 15:22 says as in Adam all die so in Christ ALL shall be made alive. And Peter tells us it is God's preference that none shall perish.