There is plenty of biblical support.
Tons of scriptures have been given to you and you can find them with a Google Search "What does the bible teach about eternal torment for the wicked dead"
The bible talks about spiritual death that define it differently than physical death. Eternal death for the wicked is defined as eternal suffering. Destruction of the wicked is defined as constant. It is a spiritual realm that is beyond the laws of physics and you cannot apply those laws to that realm. It has no end. Trying to understand it and needing an end to it, is a mental stumbling block that has resulted in these theories of annihilation.
Spiritual death is a real thing. Right now people can have full capacity of conscious awareness while being dead spiritually, and when their spirit leaves their body they will still be aware of the suffering they are in and still be spiritually dead.
Eph 2:1
1And
you were dead in your trespasses and sins 2in which you previously walked according to the ways of this world, according to the ruler of the power of the air, the spirit now working in the disobedient.
3We too all previously lived among them in our fleshly desires, carrying out the inclinations of our flesh and thoughts, and we were by nature children under wrath as the others were also.
4But God, who is rich in mercy, because of his great love that he had for us,
5made us alive with Christ
even though we were dead in trespasses.
John 5:24 “Truly I tell you, anyone who hears my word and believes him who sent me has eternal life and will not come under judgment but has
passed from death to life.
1 Tim 5:6 however, she who is self-indulgent is
dead even while she lives.
It is obvious that the bible defines a spiritual death that is not the same as a body in a casket that has no consciousness physically from the brain.
The argument about trying to define the word "destroyed" as having an end, is as weak as the attempt to say that "death" requires no consciousness. It is just confusion about defining English words in various contexts. The bible speaks in many cases of everlasting destruction, and a meaning of destruction that is constant.
But the bible is so verbose on the topic of the spiritually dead suffering forever that the average reader has no need of anyone teaching him another view which is why the majority of the modern church believes this, not because there is no biblical support but because it is the plain reading of the bible and we do not need any one to teach us that it means something other than what it says.
The stumbling block for the naturally minded man is whether it is too cruel. And this only reveals how we are soft on sin and don't see things the way God does.