I am not 100% certain, to be sure. When I discuss this topic this is what's in the back of my head: Gosh, I'll look really silly if tomorrow they unearth strong evidence that Neanderthals and Cro-Magnon interbred.
But, yes, my personal evaluation of the evidence leaves me extremely confident that Cro-Magnons and Neanderthal did not interbreed, at least to any detectable extent. For one, there are so many lines of argument against such admixture (genetic barriers, cultural barriers, language barriers, physical barriers, etc). If you do knock down one then you run into the next and then knock down that one and run into another, etc., etc.
But, more importantly, if Cro-Magnon and Neanderthal could interbreed, and if they were at all inclined to do so, then I think the evidence would be patently clear and undeniable. For one, you should have a stark genetic imprint that distinguished European populations from more distant populations. That's what I think; you don't have to agree with me.
From a scientific standpoint, I don't think that this would even be a subject for debate if not for so many people wanting so badly for it to be true. So, they grasp at the flimsiest strands of alleged 'evidence' and combine that with a tangled web of conjecture and assumptions masquerading as fact in order to fabricate the scenario they wish to be true.
But sure, I could be wrong. If the evidence ever proves me wrong I'm sure that I'll be appropriately red-faced afterward..
I don't get it. Why couldn't Cro Magnum and Neanderthal interbreed? What would prevent them from doing so? They sure looked enough like humans.