If the two species were biologically incompatible, modern human DNA should have been missing from Neanderthal X chromosomes as well. However, the analysis revealed that Neanderthal X chromosomes had a 62% excess of modern human DNA compared with their other chromosomes – a mirror-like reversal of the distribution of Neanderthal DNA in human populations.

I dunno—isn’t that still consistent with a scenario where there’s a specific incompatibility between some gene on the Neanderthal X chromosome and a human gene on some other chromosome?

Otherwise you have to have two parallel-but-opposite trends in human and Neanderthal societies, where human societies favor male offspring of human/Neanderthal unions, but Neanderthal societies favor female offspring.

(Maybe this is addressed in the full paper—I don’t have access.)