Artists originally drew the neanderthal as a sort of a stooped ape-man. The first skeletons anybody turned up in the Neander valley (Thal in German) were diseased and arthritic; more recent reconstructions show something which was clearly not one of us, but which was not altogether frightening:
The next closest hominid would have been homo erectus, which was visually and almost certainly genetically much further removed from modern humans than neanderthal:
Thus we always used to see pictures of a sort of an evolutionist chain of being showing a progression of increasingly sophisticated hominids ending with the homo erectus and then the neanderthal, and then modern man.
The assumption was that we had evolved from the neanderthal. But there was always a big mystery as to why nobody ever found evidence of crossbreeding between modern man and the neanderthal despite evidence that the two groups had lived in close proximity for long periods of time in places such as the Levant:
http://findarticles.com/p/articles/mi_m1511/is_n9_v16/ai_17199047
That presents a problem for evolutionists; in order to be descended from something via any process resembling evolution, at some point, you have to be able to interbreed with the something.
Then, starting in the late 1990s, DNA studies began to explain the mystery. Neanderthal DNA was extracted from several specimens and it turned out that neanderthal DNA was about halfway between ours and that of a chimpanzee; that plainly ruled the neanderthal out as a plausible human ancestor since the genetic gulf is simply too wide. We could no more interbreed (and produce offspring) with neanderthals than we could with horses.
http://biology.plosjournals.org/perlserv?request=get-document&doi=10.1371/journal.pbio.0020057
This leads to a logical conundrum which evolutionites so far have been unwilling to face. "Too far genetically removed to be descended from" is a transitive relationship. In other words, if the neanderthal is too far removed from us for us to be descended from him and all other hominids are FURTHER removed, then logically we could not be descended from ANY of them.
Scientists who buy into evolution so far have been unwilling to face that one. The claim you read is that we and the neanderthal are COUSINS, both descended from some more remote ancestor, which is usually given as homo Heidelbergensis, a type of late erectus:
http://anthro.palomar.edu/homo2/mod_homo_1.htm
That's basically like claiming that dogs could not be descended from wolves, and therefore they must have descended directly from fish; it's basically idiotic.
The basic reality is that there is nothing on this planet which modern man could plausibly be descended from via any process resembling evolution.