Trade with EU and Japan is good for the US and Trade with China is bad?

Yesterday in class, we’ve discussed how differently people see the impact of international trade. Here is one more example showing the controversy of the topic: according to a survey conducted by PewResearch in late 2010, 58% of sampled Americans said more trade with European nations would be good for the United States, 60% said increased trade with Japan would be good for the U.S. but only 45% favored increased trade with China. However, statistical data shows that US exports to China outpaced nearly all of the top ten export markets (including Japan and EU) from 2003 to 2012(source: USCBC).  

Why would the general public favor a particular trading partner but disfavor another? Should they? By which standard the general public may assume more trade with a particular trading partner would be good or bad for the United States? In your view, is trade beneficial for the US overall? Can we use any trade theories learnt from the class to explain the above phenomenon? Look forward to hearing your thoughts!