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Not op, but maybe it's an ESL situation.
From a strict, classical sense, liberal and conservative aren't opposed, Pprogressive and conservative are. The opposite (again in a classical sense) of liberal is authoritarian. Most of the conservative US started using liberal as a pejorative in the late 60s during the cou ter culture revolution, since it was college-age driven with liberal arts educations. ironically since in that sense it means something along to "holistic, well rounded " education, as opposed to a trade school that teaches one specific topic.
You confused me with 'liberal' in the title, and 'conservative' in the text. Surely even in the US, liberal & conservative are not the same?