Scientists are still trying to solve the mystery of our bull-like cousins' disappearance, and Scientific American rounds up more of the current thinking. One speculation:
Neandertals and moderns may have also differed in the way they divvied up the chores among group members. In a paper published in Current Anthropology in 2006, archaeologists Steven L. Kuhn and Mary C. Stiner, both at the University of Arizona, hypothesized that the varied diet of early modern Europeans would have favored a division of labor in which men hunted the larger game and women collected and prepared nuts, seeds and berries. In contrast, the Neandertal focus on large game probably meant that their women and children joined in the hunt, possibly helping to drive animals toward the waiting men. By creating both a more reliable food supply and a safer environment for rearing children, division of labor could have enabled modern human populations to expand at the expense of the Neandertals.
Are we now spelling it "Neandertal" to approximate the German pronunciation better? No doubt this impulse comes from the same people who brought you "Inka," which spelling I figured was designed to annoy Spanish-writers who rarely need the letter K.