A few of you were puzzled over this question two days ago, or at least pretended to be. So why not? For a start, the cloning process probably would require a lot of trial and error, with plenty of victims of experimentation being created along the way.
Then ask yourself some basic questions about Neanderthals: could they be taught in our schools? Who would rear the first generation? Would human parents find this at all rewarding? Do they have enough impulse control to move freely in human society? How happy would they be with such a limited number of peers? What public health issues would be involved and how would we learn about those issues in advance? What would happen the first time a Neanderthal kills a human child? Carries and transmits a contagious disease? By the way, how much resistance would the Neanderthals have to modern diseases?
What kinds of “human rights” would we issue to them? Would we end up treating them better than lab chimpanzees? Would they be covered by ACA and have emergency room rights?
We don’t know the answers here, but I would expect to run up against a number of significant fails on these issues and others.
We do, however, know two things. First, the one environment we know they could survive in (for a while) was a Europe teeming with wildlife. That no longer exists.
Second, we’ve already run the “human/Neanderthal coexistence experiment” once, and it seems to have ended in the violent destruction of one of those groups. It would be naive to expect anything much better the second time around.
Most likely the Neanderthals would end up in some version of concentration camps, with a lot of suffering and pain along the way, and I don’t see that as an outcome worth bringing about.
Addendum: If you’d like to read another point of view, there is George Church and Ed Regis, Regenesis: How Synthetic Biology Will Reinvent Nature and Ourselves.