Higher homotopy groups were defined by Eduard Čech in 1932 in a paper for the International Congress of Mathematicians in Zurich, but Alexandroff and Hopf thought that since they were abelian, they were obviously a rediscovery of the known case of homology and not the true generalization of the fundamental group. So they let him know his work was bunk, he withdrew his paper and, as I've heard, was so discouraged that he didn't do further work in the field.  It was not until Hurewicz's work that it was realized that these higher homotopy groups, though abelian, provided essentially different information than homology. (Does anyone know the earliest space which was shown to have identical homology and fundamental group, yet different higher homotopy groups?  An example is $S^2 \vee S^4$ vs $\mathbb{CP}^2$; I don't know if that is the first.)

There is some discussion [on Ronnie Brown's website](http://pages.bangor.ac.uk/~mas010/outofline/tohigherdim.html):
> On this ground, and because it was felt that the groups must be the same
> as the already known homology groups, Alexandroff and Hopf persuaded Cech to
> withdraw his paper and only a small paragraph appeared in the Proceedings
> of the Congress. Three years later, however, a Dutch mathematician, W.
> Hurewicz, published four Notes explaining the main properties of
> these higher homotopy groups, but without referring to Cech's paper, so
> they have come to be known as the Hurewicz homotopy groups. These higher
> homotopy groups became very important concepts, with many people working on
> them, despite or even because of the difficulty of calculating them for
> some standard spaces. Both Alexandroff and Hopf later admitted their mistake
> over Cech's paper. In the 1960s, when higher homotopy groups, despite their
> being commutative, had become a fundamental tool in topology and
> geometry, Hopf told E. Dyer that it showed the error of people regarding
> themselves as so great they are able to know what shall be the future.

It is also mentioned [on the nLab page for Homotopy Group](http://ncatlab.org/nlab/show/homotopy+group#history_38) and [here on Wikipedia.](http://en.wikipedia.org/wiki/Homotopy_groups_of_spheres#History)