Why are libertarians associated with the right?

[muon2]

Libertarianism strongly emphasizes freedom of choice and individual decisions in political, economic and social settings. This can be closely paired with the concept of self-reliance.

Self-reliance was a core principle of Lincoln's and so it also became part of the thinking of the early GOP. During the Great Depression, the GOP again turned towards self-reliance as one of its counterpoints to the New Deal. Reagan built much of his campaign on themes of self-reliance. Given how self-reliance is so deep-rooted in the Pub philosophy and so easily associated with libertarianism, it isn't surprising that libertarians tends to be viewed more as right than left.

[muon2]

Why are libertarians associated with the right?

Dude, it's because they are on the right.  

For example, consider this the Political Matrix scores, which can be linked to with the PM button above.  1045 posters have taken the quiz, and here are the average economic scores by party affiliation:

    Democratic        -4.13      
    Republican         +4.39
    Independent        -0.65
    Libertarian         +5.14
    Green                  -5.94
    Constitution        +4.76
    Other                -3.87
    Decline to State   -0.48

Bear in mind that positive scores are further right, and negative scores left.  Sure, it's a small (and self-selected) sample, but it should be obvious that at least among the posters in this forum, and by the standards of the Political Matrix test, Libertarians are the rightmost group.  Even Constitution party people, who are considered right-wing nuts, are not as far right as Libertarians.  This is only one data set, but I encourage to find other data and you'll see a strong correlation of self-identification with the LP with economically conservative benchmarks.

Where do you see the averages, and how different are they for the social side (what I really associate conservatism with)?

It's only since Reagan that social conservatism was associated with the Pubs and hence with the right. And its really only since the 90's that it has been strongly associated with one side as the southern Dems and their philosophical kin left that party. As I noted earlier libertarian economics has ties to the Pubs and the right back to the New Deal.