The traditional, and to many still compelling, objection to democracy as a form of government is that it is open to DemagoguerY?. It is (famously) for this reason that the UnitedStates was established, strictly speaking, as a RepubliC? rather than a DemocracY. Thus BenjaminFranklin?'s famous answer, to the question as to what sort of government TheFoundingFathers? had established, was: "A Republic, if you can keep it." A cynic would point out that DemagoguerY? and PopulisM? are two sides of the same coin. Demagogues appeal to people's baser instincts; populists allegedly appeal to their enlightened interests.
At least some arguments against democracy amount more to a complaint that the outcome of democracy is different from what the critic desired. Support for democracy may, then, sometimes not be support for the principle or theory of democracy, but rather a hopeful confidence that democracy will yield the kind of society that the supporter hopes for on independent grounds.