Beinart passes along a theory:
[T]here’s reason to believe that today, many Americans eschew the term not because they associate it with any particular unpopular attitudes or issue positions, but merely because they’ve only heard it discussed negatively. In a thought-provoking 2013 paper, Christopher Claassen, Patrick Tucker, and Steven S. Smith of Washington University in St. Louis note that although most Americans prefer the term “conservative,” those same Americans are “remarkably consistent” in telling researchers that they prefer liberal policies. How come? One reason may be that “conservative” has positive “extra-political” associations. To many Americans, it connotes “caution, restraint and respect for traditional values,” positive attributes irrespective of one’s views on specific policies.
But even more important, Claassen, Tucker, and Smith suggest, may be the negative way in which “liberal” is publicly discussed. “When certain labels are emphasized or favored by political and media elites,” they write, “the public is more likely to identify with them than others. Public framing often promotes the term ‘conservative,’ while the term ‘liberal’ is used with much less frequency and has long had a more negative connotation.” Part of the reason Americans consider liberal an epithet, in other words, is because they mostly hear it used as an epithet.