At some point during the evolutionary chain (according to the theory) life became more complex.
Now surely, homo sapiens and the Neanderthal have much in common. Much more in common, than say a man and horse. In fact, the scientific communities assumptions on the Neanderthal have changed greatly over the years. According to the evolutionary theory itself, homo sapiens and Neanderthal are related, regardless of what DNA evidence is presented to the contrary. This is obvious to any observer - the two have incredibly similar features.
Modified reconstruction of Gibraltar Neanderthal child
So why does the scientific community invest so much time and energy to try to divorce the two?
Homme de Néanderthal
Perhaps this chart will help.
The two are certainly related, and share a common ancestor. I think the issue being discussed here is the amount (if any) of intermixing between modern humans and Neanderthal.
Many think that after the separation there was essentially no intermixing and that Neanderthan eventually died out.
Source: http://wwwrses.anu.edu.au/environment/eePages/eeDating/HumanEvol_info.html