Wayne Grudem (Systematic Theology, p1150) notes the following arguments that are advanced in favour of annihilationalism:-

1. the biblical references to the destruction of the wicked, which, some say, implies that they will no longer exist after they are destroyed (Phil. 3:19; 1 Thess. 5:3; 2 Thess. 1:9; 2 Peter 3:7; et al.);
2. the apparent inconsistency of eternal conscious punishment with the love of God;
3. the apparent injustice involved in the disproportion between sins committed in time and punishment that is eternal;
4. the fact that the continuing presence of evil creatures in God’s universe will eternally mar the perfection of a universe that God created to reflect his glory.

In response to (1), Grudem claims that the passages which speak of destruction do not necessarily imply the cessation of existence.

In response to (2), Grudem says that the same argument could be mounted against any form of divine punishment against sin.

In response to (3), Grudem thinks that it wrongly assumes that we know the depth and extent of sin, and therefore the amount of punishment due to it.

In response to (4), the divine perfections would be marred only if evil remained unpunished and unvanquished.

Grudem rightly notes that we cannot fully fathom these truths, and that any contemplation of them should lead to a deep sense not only of inadequacy but also of sorrow and profound concern (cf. Eze 33:11; Mt 23:37f; Rom 9:2).

Grudem would agree that the ultimate question in this, as in all other matters concerning the things of God, is, ‘What says the Scripture?’  In my view, he has not demonstrated that Scripture forces us to repudiate annihilationalism.