You can support common markets while still raising an eyebrow at some of Brussel's decisions.
France is trying to prevent Americans from publishing true facts in the states, because misguided Frenchmen might accidentally seek such facts out and read them.[0]
Also, it's not altogether clear that any good long term compromise has been found to balance the needs of the strong economies alongside the more fragile ones.
You staved off Grexit, but retained the powderkeg of local fiscal policy with central responsibility for solvency of members.
Now, if I were in the UK, I probably would have seen these as secondary issues to the value of the common market. But worrying about concentrated power doesn't seem alien to me. And given the UK and EU are both in the WTO and so culturally related, it's not like I'd fear both sides will instantly revert to quotas, 1000% tariffs, and random visa denials.
Ok, ok, academic leavery aside, the mainstream leave does seem related to immigration, and that's troubling even if leave could be justified on other grounds. Nate Silver had a comment on the 538 podcast, something like, "We hold up liberal democracy as the pinnacle of governance, but it seems to have a systemic problem with immigration." That seems troubling, and I'm not sure entirely what to make of it yet.
[0] http://www.voanews.com/content/google-appeals-french-order-f...