I will describe two sharp puzzles suggesting a possible mismatch between the current hierarchical merging paradigm and observations of evolving galaxies. Current models predict that the z ~ 4-8 universe should be a time in which the most massive galaxies are transitioning from their initial halo assembly to the later baryonic evolution seen in star-forming galaxies and quasars. Instead, massive galaxies appear to exist impossibly early, before their halos should even have been able to assemble. Further, small halos should have generally formed earlier than larger halos, yet the observed hierarchy in galaxy formation is inverted, with more massive galaxies completing their growth earlier. After describing these puzzles, we will consider whether hierarchical merging is truly inconsistent with observation or whether other explanations might be more likely.