First of all, the scripture is very clear in regards to Hell and Heaven being eternal.  The word "destruction" does not mean annihilation, but it generally implies that it is ongoing.  The verse in Mathew 25:46 is the same word for eternal life and eternal punishment.  If Hell is only temporal, then Heaven would also have to be only temporal since it uses the same word "aionios."  Also, the same word “eternal” is used in 1 Tim 1:17 of our eternal King.  So if hell is not eternal, then God isn’t either.
 
Also, there are all these verses that say eternal, fire not quenched, everlasting fire, fire that shall NEVER be quenched, tormented day and night, forever and ever, shall not see life, resurrection of life and resurrection of damnation.   These are the verses:
 
Mt. 25:41, Mt. 25:46; John 5:29, John 3:36; Rev. 20:10, Rev. 14:9-11; 2 Thes. 1:9; Dan. 12:2; Mark 9:43; Mt. 18:8, Mt. 13:30, Mt. 13:49-50; Luke 3:17; Jude 7; John 4:14, John 5:24; Rom. 2:8-9.
 
If you think about it, why would God simply annihilate someone?  There is no justice in that. God is a God of Justice and Righteous Judgment.  (See:  Ps. 96:10, Ps. 89, Acts 17:31, Ps. 96:13, Deut. 32:4.)  Also God’s wrath is released upon sin  (See John 3:36, Ps. 90:7-11, 2 Thes. 1:8, Rom. 1:18, Rom. 5:9, Ex. 15:7, Prov. 11:23, 2 Pet. 2:9, Jer. 4:4)  There are many verses regarding varying degrees of punishment.  How can you have varying degrees if one is annihilated?  Verses – Mt. 23:14; Mt. 23:15; Mt. 10:15; Luke 12:47, Heb 10:28-29.
 
The rich man in Luke 16 thirsted in the torment of the flames, he was still there existing and experiencing torment.  Is. 14:9-10 says, “Hell from beneath is moved to meet thee at thy coming…they will say, art thou become weak as we?”  Also in Ez. 32:21 “They shall speak to him out of the midst of Hell.”  How could they speak if they didn’t exist?
 
Jesus illustrated about worms, as in those days it was common to see a dead animal being eaten by worms.  When the flesh is consumed, the worm dies.  They understood that, so where “their worm dies not” tells them the flesh is never consumed. In Is. 14:11, it uses the word maggot..."is spread under thee, and the worm covers thee.”
 
Annihilationism is not accepted by all mainstream Christian theology (Methodist, Baptist, assembly of God, etc.)  The great men of the past and present, such as, Jonathan Edwards, John Wesley, John Calvin, John G. Lake, John Bunyan, Charles Stanley, Billy Graham, Franklin Graham, Dr. James Kennedy, Chuck Smith, Charles Finney, A.W. Tozer, John MacArthur, etc. all believe in eternal punishment, not annihilation.
 
There are additional verses mentioned in my book under the Research chapters.