Nurture is the major factor in nearly every aspect of human achievement. Alternative explanations justify genocide, neglect, and let adults off the hook.
If some part of the gap in achievement is genetically determined (which by all measurements is the case.) than there is no way to close that gap. Children from poor parents stay poor, poor communities can not move up etc.
What's proposed is that the only possible way eliminating differences is eliminating people (in either direction.). Of course this does not infact justify genocide or any of the sort, but that's the argument.
While possibly true, none of those claims have any bearing on whether or not those alternate explanations are false.