One thing no Christian can deny is that God is perfectly just and Holy. He is without sin, His judgments are without bias, and His wisdom is without question. When all is said and done, however He deals with man, we must accept is the most perfect way to deal with man that can be imagined.
For us as Christians, this can only mean good things. While we were due His wrath, He sent His Son to receive our penalty on our behalf. This not only erased our debt, but ultimately, guarantees us eternal life in a Kingdom we literally cannot imagine. But what about the impenitent? Those who refuse to come to faith in Christ will not inherit eternal life. Instead, their ultimate penalty is what the Bible calls the "second death".
Keeping God's perfection in mind, many suggest that this "second death" cannot possibly be the lake of fire and brimstone where the impenitent suffer torment day and night forever and ever with no rest, as Hell is described in Revelation 14:9-11 and 20:7-15. This, they say, would actually be very unjust.
But perhaps you've already spotted the flaw in the argument. See, when an Annihilationist states the argument, they will typically omit Biblical descriptions of what Hell is like. Not that they never address it at all, but they would never state this particular argument as I just did. Rather, they will focus on Scriptures which describe God's justice, His love, His Holiness etc., and use these attributes of God to suggest that Eternal Conscious Torment cannot be true, as this would be very much unjust and unloving.
The problem we have, however, is that the Bible does seem to describe Hell as a permanent place of conscious torment, even to the extent where some people will suffer more than others (e.g. Matthew 10:15; Mark 6:11; Luke 10:12-14; Luke 12:47-48). Avoiding this requires some very selective application of terms like "forever" and "eternal". Take, for example, Matthew 25:46: "And these will go away into everlasting punishment, but the righteous into eternal life." It is impossible to consistently interpret only one of these as literally eternal, but the other as temporary.
With this in mind, it's quite clear that Eternal Conscious Torment is the Biblical view. But then is God unjust? Certainly not. Rather, we are unjust. See, Hell seems awful to us, and indeed, it is awful. It wasn't even designed for us! When God casts man into Hell, He doesn't say "Depart from Me, you cursed, into the everlasting fire prepared for you", but "Depart from Me, you cursed, into the everlasting fire prepared for the devil and his angels" (Matthew 25:41, emphasis added). Death, of any kind, is not something God takes pleasure in. He wants everyone to be saved (1 Timothy 2:4), He wants no one to perish (2 Peter 3:9), and He takes no pleasure in the death of the wicked (Ezekiel 18:32; 33:11).
Oh, but He will kill them! In Scripture, many are given the chance, even the express command delivered by a prophet, to repent, yet they do not take it. So what is God left with? Ultimately, the answer is the second death, but before that, there is the first death! And how often do we look back at that and think "wow, God, why?" Why did you flood the whole Earth, sparing only 8 people? Why did you turn Sodom and Gomorrah into an ashy pile of rubble? Why did you kill the firstborn of every Egyptian household in one night? But you know why. "For as the heavens are higher than the earth, So are My ways higher than your ways, And My thoughts than your thoughts." (Isaiah 55:9).
So what if you do think Hell is unjust? You're going to, because it's objectively undesirable. I don't like the idea of anyone suffering forever, even if it's just a mild cold, and unfortunately, I have grandparents who are more than likely bound in chains awaiting the day they will be cast into the accursed lake. I would love to be an Annihilationist. But knowing that God's thoughts are above my thoughts, and His ways are above my ways, I will never be able to say "God, if Eternal Conscious Torment is true, you're not really just." In this case, I have to admit that I am the unjust one. Here I stand, a sinner before the Holy God, trying to choose the punishment I deserve? And having received a full pardon, I again turn my face against God and accuse Him of being unjust for daring to judge others? Well then why don't I just apostatise fully? If I can tell God "you're unjust for condemning the impenitent to Hell", why can't I equally accuse Him of injustice for condemning my sin at all?
The obvious answer is because that's not the kind of consistency I want. I could be consistently unjust, condemning God for His judgment and walking away from Him entirely, like some arrogant atheist who likewise thinks he gets to decide the morality of Hell, but all that ultimately does is drink judgment upon myself. A judgment which I am unable to bear. Instead, a better option is to recognise the severity of my sin - even if I cannot yet comprehend it. If God says my sin is worthy of His everlasting wrath, so be it. Who am I to tell Him He's wrong?
And who are you?
As Christians, we should all take God's justice as our starting point, but this doesn't give us the right to use our depraved view of justice to form our own doctrines. Instead, it should prompt us to take God's instruction as with all things. Remember, we're sinners who need salvation. What did God save you from? Would you have left that sin if not for His instruction? I wouldn't. Just as we receive God's instruction to repent of our past sins (and the sins we still struggle with), we should recognise that the desirability of Annihilationism does not overrule the justice of Eternal Conscious Torment. Instead, it should motivate us. It should motivate us to desire the salvation of those heading for eternal doom, and to actively seek it. Let us not spend one more minute questioning the justice of the Almighty, and instead rejoice in His mercy on us, as we seek to bring it to others.