In other words, libertarians don’t oppose democracy (in the conventional sense) because they hanker after autocracy; they oppose democracy because it is too much like autocracy.
This is a core problem with many critics of libertarianism (and with the anti-Chicago boys from the Friedman-Chile-Pinechot contingent of argument). Basically people who are democracy advocates have a hard time accepting a premise that rather than use government or votes to design social systems the alternative is not we must now use centralised autocratic/technocratic controls. You use nothing at all. No one is in charge or if any government or state policy is involved it is very minimal (think free speech protections, sans FCC style censorship).
One core reason is that even very well-intentioned state interventions tend to end up captured by other powerful agents in the system (church, corporation, unions, etc) because they have very little actual control over the system as a whole and thus the top down regulatory state has very little means to discern the proper levels of control or even the levers that it should use in the first place to create that control. It ends up generally being worse than having a market "rule" as a result.
In any case, being opposed to democracies, or generally finding that majoritarian rule is a poor form of democratic government, is not the same as "I want more dictators!". I don't go around supporting Gaddafi-esque regimes. I of course also don't propose that we bomb them out of office but say we are on a "humanitarian" mission either. If you really wanted them out, say so, design the plan and followup accordingly and come back to us then. Don't say that we're dropping bombs to help people. Because that doesn't help. Sigh. I digress. The statement above is a fair reflection of what we're looking at when we see "democratic" systems. We are seeing autocratic behavior exercised through majority will. As it is, there are plenty enough people that would excise from any and all of us core protected rights (free speech, free press, freedom of religion and conscience, etc) if it were up to them and so unsurprisingly there are a whole range of issues upon which the majority is permitted, by the magical mechanism of voting, to impose its will upon a minority, be they meddling in private behaviors, consensual transactions, business licensing, and so on. Very little of this serves any practical purposes or fosters a free society.
I'd hardly say that this reflects well on "democracy" as conceived of a mandate of collective wills as opposed to "democracy" conceived of a collection of protected rights and core values that comprise a free society and its basic liberties. The latter is more important ultimately.