They claim that the 'violent, vengeful God of the Old Testament' bears little resemblance to the 'loving God of the New Testament'.
This is claimed to be an 'inconsistency'.
The answer I suggest offering, from a Christian viewpoint, is to some extent unsatisfactory but it rather wrecks the claims of non-believers.
Simply point out to such people that a considerable number of the tribes of The Middle East practised child sacrifice in their worship of Moloch, Baal and Astarte. The Jews did not - and were punished when they strayed.
The reason why this argument is only peripheral for Christians is because the main reason is more to do with the nature of idolatry.
Those who argue for the variation between the testaments - and more than a few in the Church - are in for a rather large shock when The End Times predicted in Matthew 24 inter al come to pass!
