Tyler Cowen considers reasons why we wouldn’t want to clone neanderthals. There are many ethical questions on how we would deal with the offspring:

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.