Greetings Eja... couple questions now...
Why is the "Out of Africa" theory a trap? It's a theory isn't it? People can put whatever spin they want on a theory for their own purposes, but ultimately a theory ought to stand or fall based on the amount of evidence there is for it. As I understand it there are two main theories of human evolution currently making the rounds: out of africa (which most scientists lean towards), and multi-regional evolution (supported by a minority). From my admittedly layman's perspective, there seems to be more evidence for the out of africa theory. ALL of the EARLIEST hominid remains were found in Africa; later, they are found around the world. So, logically, it seems that hominids left Africa and settled in other regions of the world. ALL of the EARLIEST homo sapiens sapiens remains were found in Africa; later, they are found around the world. Hence, it seems that homo sapiens left Africa and populated the world. Then, there are the mitochondrial DNA studies that purport to show (I say purport because I myself am not at the moment qualified to undertake a mitichondrial DNA study and analyze the results myself) that all modern humans are descended from a small population of Africans who left East Africa approx. 80-100,000 years ago.
I'm not sure how Europeans can be said to have the same characteristics as neanderthals. Neanderthals had larger brains than contemporary humans, with some specific parts of the brain larger and some smaller. Europeans on average have the same size brain as Africans, with the same general size of the respective parts of the brain. Neanderthals looked different enough from modern humans for them to stand out in a crowd if there were any pure neanderthals left. Europeans are descended from neanderthals "by their own admission" - what does that mean? How would they know whether or not they are descended from neanderthals anyway? Unless you mean the study of the "hybrid" neanderthal/homo sapiens bones, which MAY indicate that the two sub-species interbred, which COULD have given rise to partly neanderthal-descended europeans - although the German scientist responsible for the hybrid bone finds has been accused by some of dishonesty. Sure, any scientist could be dishonest, but why dismiss the findings of a whole heap of people who do NOT have specific charges of academic dishonesty pending against them, while accepting the findings of one person, who does? I'm not saying either one is right or wrong, I just don't see the logical basis for accepting one and dismissing the other.
Ultimately I don't accept or reject a theory based on whether I personally "like" the theory or not, or whether it gibes with my already-formed worldview. Theories are either relatively inaccurate or relatively accurate explanations for the way the world is, whether they are considered relatively inaccurate or relatively accurate should depend on the amount of evidence for them, and how well they can accurately predict things based on their suppositions - nothing else.
It is possible that humans were genetically engineered by alien beings. There are theories that say so, and there is nothing inherently impossible about it. I don't particularly like the idea that there might be extremely powerful alien beings out there manipulating our genes for their own ends, but if I saw the amount of evidence for that theory that I do for the out of africa theory, I would lean towards accepting it, as I lean towards accepting the out of africa theory today.
Why would any African support the theory? For me, because it seems to be the theory I've seen so far, that is best supported by the evidence I've seen so far, at least as it has been presented to me and as I understand it. That doesn't mean I think the theory is "true", just that I think it seems to be the theory that gibes most with the evidence as we know it today. Supporters of other theories should simply make known the evidence for these other theories and let people decide based on that. Theories (at least in the physical sciences) are supposed to fit with the world as we see it, not with our ideologies.
Now is it POSSIBLE that Euros are hybrid neander/homo sapiens whereas Africans are pure homo sapiens? Sure. And there seems to be at least one interesting piece of evidence to support it - the "hybrid" bones. It's also a very controversial piece of evidence, but a piece of evidence still.
Even if that were true, though, I don't see how it alters the basic parameters of the out-of-africa theory. According to the sapiens/neander hybrid theory, Neanderthals, whose ancestors most likely came from Africa, mated with homo sapiens, whose ancestors most likely came from Africa, to produce Europeans, or red-haired Europeans or whatever sub-group they produced. The ancestors of both groups still originated in Africa.
As for knowing how hairy or hairless or what colour skin people/hominids had, I don't see how you can do that in the absence of mummies or similarly preserved bodies. Bones won't tell you what colour skin people/hominids had. You would have to guess that based on the environments they inhabited, how long they would have had to adapt to those environments, and so on.
Also if neanderthals and homo sapies mated and had hybrid offspring who were themselves fertile, then they could not be considered two different species, as the definition of species involves individuals of the same species being able to mate and produce fertile offspring (horses and donkeys are considered different species because although they can mate and produce offspring, the offspring are infertile 99.9% of the time.)