Why did the Lord Buddha criticize natthikavādaṃ (moral nihilism)? In SN 24.5, the Lord Buddha criticized the following doctrine called "natthikavādaṃ": 


  There is no benefit in giving, sacrifice or offerings. There’s no fruit or result of good and bad deeds. There is not this world or the
  other world. There are no duties to mother and father. No beings are
  reborn spontaneously. And there’s no ascetic or brahmin who is well
  attained and practiced, and who describes this world and the other
  world after realizing it with their own insight.
  
  This person is made up of the four primary elements. When they die, the earth in their body merges and coalesces with the main mass of
  earth. The water in their body merges and coalesces with the main mass
  of water. The fire in their body merges and coalesces with the main
  mass of fire. The air in their body merges and coalesces with the main
  mass of air.
  
  The faculties are transferred to space. Four men with a bier carry away the corpse. Their footprints show the way to the cemetery. The
  bones become bleached. Offerings dedicated to the gods end in ashes.
  Giving is a doctrine of morons. When anyone affirms a positive
  teaching (atthikavādaṃ) it’s just baseless, false nonsense. Both the
  foolish and the astute are annihilated and destroyed when their body
  breaks up and don’t exist after death.


According to SN 24.5, why did the Lord Buddha criticize natthikavādaṃ (the doctrine of disbelief)?
The answer is present in the same sutta:


  “When form exists, because of grasping form and insisting on form, the
  view arises: ‘There’s no meaning in giving, sacrifice, or offerings. …
  Both the foolish and the astute are annihilated and destroyed when
  their body breaks up, and don’t exist after death.’ When feeling …
  perception … choices … consciousness exists, because of grasping
  consciousness and insisting on consciousness, the view arises:
  ‘There’s no meaning in giving, sacrifice, or offerings. … Both the
  foolish and the astute are annihilated and destroyed when their body
  breaks up, and don’t exist after death.’


In other words when self identification with forms,feelings,perception,consciousness and/or volitional formations occur such a view as highlighted by you also occurs.

I think the the wrong view of moral nihilism gets generated when we say that every self ceases to exist after death(i.e body and self are same) or that every self lives for eternity(i.e body and self are different). In both the case following holds true :


  ‘There’s no meaning in giving, sacrifice, or offerings. There’s no
  fruit or result of good and bad deeds. There’s no afterlife. There are
  no duties to mother and father. No beings are reborn spontaneously.
  And there’s no ascetic or brahmin who is well attained and practiced,
  and who describes the afterlife after realizing it with their own
  insight. This person is made up of the four primary elements. When
  they die, the earth in their body merges and coalesces with the main
  mass of earth. The water in their body merges and coalesces with the
  main mass of water. The fire in their body merges and coalesces with
  the main mass of fire. The air in their body merges and coalesces with
  the main mass of air. The faculties are transferred to space. Four men
  with a bier carry away the corpse. Their footprints show the way to
  the cemetery. The bones become bleached. Offerings dedicated to the
  gods end in ashes. Giving is a doctrine of morons. When anyone affirms
  a positive teaching it’s just baseless, false nonsense. Both the
  foolish and the astute are annihilated and destroyed when their body
  breaks up, and don’t exist after death’?” 


The truth there is that there is no permanent , unchanging self.  What is happening is Clinging to forms,feelings,perceptions,consciousness and/or volitional formations. These Clingings are not unconditional. Craving gives rise to clinging. This is the midddle way. Depending upon conditions clinging ceases. Depending upon conditions clinging arises. This is the Dhamma. To those who believe in Self it would appear Self arises and ceases which is self contradictory as self is permanent and unchanging. Morality based upon the assumption that Self and body are the same results in moral nihilism. Morality based upon assumption that Self and body are different leads to moral nihilism. 

EDIT: I have found another Sutta(saṃyuktāgama 297) to support my answer.
Following quote illustrates the point I have been trying to make:


  “What is the great discourse on the emptiness of dharmas? It is this:
  Because this exists, that exists; because this arises, that arises.
  That is to say: Conditioned by ignorance, activities arise; because of
  activities, consciousness arises, and so on …, and thus arises this
  whole mass of suffering.
  
  “Regarding the statement conditioned by birth, aging-and-death arises,
  someone may ask: Who is it that ages-and-dies? To whom does
  aging-and-death belong?
  
  “And he may answer: It is the self that ages-and-dies. Aging-and-death
  belongs to the self; aging-and-death is the self.
  
  “To say that soul is the same thing as body, or to say that soul is
  one thing and body another, these have the same meaning, though they
  are expressed differently. For one who has the view which says that
  soul is the same thing as body, there is no point in the noble life.
  And for one who has the other view which says that soul is one thing
  and body another, there is also no point in the noble life. Following
  neither of these two extremes, the mind should move rightly toward the
  Middle Way.