Now, contemporary EU on the other hand has a vastly different and divergent history from that of the U.S. and Europeans, generally speaking, aren't as skeptical of their government as Americans are. Also, EU leans more to the left (generally speaking) relative to the United States, most "right-wing" parties in the EU would be considered to be slightly left-of-center if they were based in the U.S. [1]
Now, with that out of the way, to address your question -- both places have vastly different history and the divergent histories has given birth to vastly different cultures, helped by the fact that they're separated by the second-biggest body of water on the planet, making it even harder for inter-culture interaction. Right-leaning countries, like the U.S. for example, generally advocate for more free trade, less regulation and less taxation which is directly antithetical to the core principles of left-leaning countries, like the EU-bloc for example. [2]
[0] http://www.tep-online.info/laku/usa/rights.htm [1] https://en.wikipedia.org/wiki/Left%E2%80%93right_political_s... [2] http://www.pewresearch.org/fact-tank/2016/04/19/5-ways-ameri...