Re:antireincarnation
The souls of animals and morality.
Problem that arises is that animals are basically damned to hell in the mainstream Abrahamic model if you take it seriously. There is clearly more to it, or else, given that the 'animals nature' in mankind itself is seen to be evil ("sins of the flesh" et al), then animals by their nature are beings destined to hell. There is no way around it under the typical pretenses. (things get even worse if you believe that belief and morals are salvation, because animals don't believe anything or follow any moral systems, they are purely innocent).
If animals don't have souls however, then things are just strange, and provokes the question of whether we ourselves even have souls, or what a 'soul' even is.
Also, morality. If morality (in the metaphysical sense, not in the sociological or anthropological/cultural) exists, then any kind of being would be subject to that, God as much as you or I. Considering how terrible God is in the Bible, that cannot be a source of morality. Morality has to come from some metaphysical law relating to the relation of things in the material universe. The Dharmic view explains this very eloquently and is more reliable in grounding this fact.
Without some kind of interlocking concept such as reincarnation (which solidifies the reality of the soul through the mode of Karma), then morality itself cannot be said to have a stable existence - whether in a Christian or Atheist worldview makes no difference here.