BambinaJAS In my household of three postgrads, two of us voted Leave. We did that whilst we lived (and dh worked) in Brussels. His stint seconded to the EU made him realise what an awful organisation it is; how corrupt it is; and how self serving it is.
People voted remain because in many cases, they enjoyed the so called status quo. However, what they failed to realise is that with the EU, there is no status quo. It is not a benign organisation, you only have to look at the treatment of Greece, Italy and Cyprus for that, and a generation of people with no future. The same holds true to an extent in parts of France. Some voted Leave precisely because they didn't like what they saw and heard, and because the EU is a gravy train for many, which we all fund. I fail to see how a Eurocrat or fonctionnaire in Brussels can possibly make a better decision about what affects a locality, than the local people themselves. I do not want to fund that extra (and expensive) level of bureaucracy.
Trump was right about certain NATO Allies not paying their dues, especially Germany and Belgium. This is a call that has been made by various U.S. Presidents, including Obama at the Caerleon Summit. Trump was just less diplomatic in how he phrased it; but it did work, eventually.
As for the Brits not being involved in European defence, we are, via NATO. There is no need for the EU to have Armed Forces. The EUMS directs the EU Military effort (such as it is), and that is run on NATO lines anyway. Any attempt at an EU Military will dilute NATO, as there won't be any more Forces, just a third hat for them to wear, along with their national and NATO ones.
The EU is part of the problem, it is not the solution. The answer is not, and never will be, more Europe.