The UK was never a very convinced member of the EU, so Brexit is not a good example. But more importantly, the EU is not falling apart, it is merely facing a crisis. A pro-EU US administration could help to save it while Trump will likely accelerate it's decline.
On the contrary, a Trump presidency and the Brexit actually creates the external counterparts that is needed for people to gather around. Adding to that, the US feels like a very alien culture nowadays, reenforcing the feeling of being somewhat more similar to each other in the EU.
If the EU, designed to be the counterbalance to the United States, is so delicate that it lives or dies based on the decisions of one man that doesn't even live there, it is falling apart.
There's no way around this; if it's gotten to that point of illness it has already proved itself extraordinarily weak. Blaming Trump for pushing it over the edge is just a politically-convenient privileging of the numerous other forces that must be pushing it over, and it's hard for me to believe that Trump is even in the top 10 reasons, especially given the lateness of his entry on the scene. Do we seriously believe that things would be so much better if Trump had not won? It's not like Obama particularly managed to hold it together or anything.
> If the EU, designed to be the counterbalance to the United States
That was never the reason for the foundation of the EU. If that's the level of your understanding of European politics, I can't take you seriously anymore.
If the EU fails, which I doubt, Trump would have played a minuscule role, exacerbating existing tensions. I actually expect quite the opposite from a Trump presidency, though unintended by him.
The EU is designed entirely for internal reasons: to end the cycle of great wars between France, Germany, Russia and Britain over resources and arable land. The basic idea is that you don't need to fight over coal and steel, if you can just buy it. Protectionism, by design, leads to conflict. This could be intentional, expecting to win that conflict, but for Europe, with several adjacent powers of similar strength and modern weaponry, it was obviously not working out well.
American influence has actually been instrumental in getting the project started[1]. 'Europe' doesn't have any geopolitical or military ambitions, and as so many member states are NATO members, it tends to follow American interests in these matters.
> designed to be the counterbalance to the United States
That would be news to me. The EU has never claimed it is a counter-balance to the United States. Some people argue for a stronger, independent EU, but this is surely not the primary purpose of it.
The EU will fall apart, it's only a matter of time. The Euro as a currency is not sustainable and the moment a net paying country moves out of the Euro, the EU will disintegrate for sure.
At the moment the Euro is just a mechanism to transfer wealth from the northern countries to the southern countries and to make exports easier for Germany. Greece and Italy would be able to import much less goods from Germany if they had their own weak currencies, so would be bad for German exports, but would allow Greece and Italy to recover their economies by devaluing their currencies which would result in decreasing imports, increasing exports.
In the current situation a country like Greece will never recover and Northern European countries will pay perpetually. The same stuff could happen with Italy, Spain, etc...
> mechanism to transfer wealth from the northern countries to the southern countries and to make exports easier for Germany
I agree that it works very well for Germany. This, by the way, also implies that the transfer of wealth is not a problem. It is economically reasonable for Germany to pay and the Greek people, for instance, have clearly stated that they want to stay in the Eurozone. Additionally, the Euro can be fixed, it is just currently not politically possible to take the required actions, because the current state of affairs is "good enough". This will change if the Euro is seriously threatened.
