Too general, mon capitaine! Left Europeans like the liberal side of the USA. Beat poetry, The Summer of Love, Berkeley in the Sixties, the Civil Rights Movement, the anti-war movement were great inspirations for the student uprising and eventual political and social reforms that significantly reshaped Western Europe after 1968.
What left/liberal Europeans don't like is the American mainstream represented by the political right. Not only do we mistrust American claims for superiority. It is foremost the religiosity pervading large parts of America's self-conception that estranges a continent based on secularism (especially your country, Georges
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The combination of trigger happy military force and religious rhetoric of the Bush years has damaged America's image abroad. Whether US citizens care or not. For those who might have forgotten: During the Clinton years, the US were very popular amongst Europeans.
Europeans don't like Obama because they think he's a brilliant politician (most people are too uninformed to jump to any conclusions about his performance). They like him because he appears to be more modest and more sophisticated than the Bush crowd.