All authorities agree the Neanderthal is roughly halfway. If the human-chimp difference is 2%, the human-Neanderthal difference is 1% and not .5%. For that matter, even a quarter of the difference between humans and chimpanzees is a gigantic genetic difference and caucasions being in any way descended from such a thing would produce huge differences between whites and other races, which is definitely not the case.
Either way, a 1-4% admixture of something 99% (or 99.5%) the same is not going to lead to a huge genetic difference.
And how do you explain the existence of a creature that is (supposedly) halfway between humans and chimps?
God playing a joke? An experiment? Giants in the Earth?
You have an explanation? Considering just how whackadoo loony your other ‘explanations’ are (for the Big Bang and suchlike) this should be a doozy!!!!
:)