Where do people get the idea that minarchism equals rightism? I mean, the "right" was originally monarchists; the term started during the French Revolution. I can understand how leftism grew out of the revolutionary movement? But come on. Minarchism is NOT "right".
Look at the process over time:
In the US, the founding fathers established a government that rejected monarchy, divine right to rule, etc. Its focus was federalism and a limited federal government. This was the 1780s
Over time, as some people became interested in altering this system, others resisted, hoping to conserve the system as it was. These are conservatives.
As Jerry pointed out, in general, conservatives are considered "right" because of the location of groups in the assemblies during the french revolution, where those on the right side (as conservatives) were opposed to republicanism (which they associated with the tumult of the English gov't under Cromwell) and favored a monarchy. Those on the "left" (especially in "the mountain") then were those who were populists and republicans who, when they gained power used the terror and the committee of public safety to behead thousands. The context is entirely different in America...first and foremost, the US has never had a king.
The terms "right" & "left" are applied in american politics out of convenience--they are simply distinctive labels, not because american conservatives are or have ever been the same as french conservatives in the 1790s. The same goes for the american left--they are not the same as the leftists of the french assemblies.
An american conservative is in favor of the repuclican government that was originally established under the constitution, whereas american liberals are in favor of extremely loose interpretations of the constitution, which expands the power of the federal government. Therefore, the conservative "right" in the US is in favor of conserving the authority of the constitution, our original form of government, which heavily restricts the power of government. The "left" tends to make moves to degrade the authority of the constitution, which expands the federal government.