I'm sorry, the Bible simply does not say that evildoers are immortal. If you think that the Bible says this, please show the Chapter and Verse. Destroyed forever means to be destroyed and remain destroyed forever. It does not mean a continuing state of destroying which never results in destruction. That could not be called "Destroyed". If the end of destruction is never reached, then it is not destruction.
But the simple fact is that the Bible never says that evildoers are immortal. The Bible says that the GIFT of God is eternal life in Christ Jesus our Lord. Those who reject Christ will not receive the Gift of eternal life. They will not receive immortality.
All human souls are immortal.
Mark 9:47-49
And if your eye causes you to sin, pluck it out; it is better for you to enter the kingdom of God with one eye than with two eyes to be thrown into hell, 48 where their worm does not die, and the fire is not quenched. 49 For every one will be salted with fire. rsv
The second death is the lake of fire.
Revelation 20:14
Then Death and Hades were thrown into the lake of fire. This is the second death, the lake of fire; 15 and if any one’s name was not found written in the book of life, he was thrown into the lake of fire. rsv
Spiritual life and spiritual death. Spiritual death is the loss of eternal life with God.
Eternal life with God or eternal death with Satan. Both states are forever.
Jesus said the rich man was being tormented by a flame in Hades. We know it is hell because Jesus said that he could never leave there. Please note that the rich man's soul/spirit was not annihilated by the flames.
Luke 16:22-25
The rich man also died and was buried; 23 and in Hades, being in torment, he lifted up his eyes, and saw Abraham far off and Laz′arus in his bosom. 24 And he called out, ‘Father Abraham, have mercy upon me, and send Laz′arus to dip the end of his finger in water and cool my tongue; for I am in anguish in this flame.’ 25 But Abraham said, ‘Son, remember that you in your lifetime received your good things, and Laz′arus in like manner evil things; but now he is comforted here, and you are in anguish. 26 And besides all this, between us and you a great chasm has been fixed, in order that those who would pass from here to you may not be able, and none may cross from there to us.’ rsv
John 5:28-29
Do not marvel at this; for the hour is coming in which all who are in the graves will hear His voice 29 and come forth—those who have done good, to the resurrection of life, and those who have done evil, to the resurrection of condemnation. nkjv