Homo Sapians and Neandertoles in Israel

It is a commonly accepted fact that homo sapians and neandertols crossed paths as they both lived simultaneously. Homo sapians would have had absolutely no qualms whatever about having sex with neander toles. It makes much more sense than the unnatural urge to inbreed within your own population. If this is true, then our traditional of ourselves as an advanced species compared to the rough old neandertoles, is a completely pompous modern view. We are unsure as to whether homo sapian and neandERTols actually lived side by side in israel. It could very well be that different populations of each species occupied sites in that area at different times.