The head and neck structure of Neanderthal Man is quite different than Homo Sapiens Sapiens. It's difficult to believe they could have interbred successfully, without the offspring being seriously physically deformed. Sharing similar genes, doesn't mean interbreeding, merely having similar ancestors. The great apes and man share most genes. If Africans, don't have the same genes as EurAsians, it just might be that the out of Africa hypothesis of Evolution isn't true, and there were separate evolutionary events, that resulted in the different humans alive today, that are from completely separate evolutionary sources.