Do you think that the British Isles are a part of Europe?

Of course, the French and Germans each think that as well.

The EU can be summed up in a simple statement: The French think it will bring peace, help reign the Germans under control, and prevent the Germans from ever again invading. The Germans think the union will allow them to dominate France and be able to exert their influence throughout Europe (which is sort of a little bit true in some ways).

Now, what do the British have to gain?
Historically the British were always trying to divide Europe and prevent it from becoming unified because they feared it would become too powerful and be able to dominate over Britain.

 

That the UK did, for a good while, belong to the EU, should show you that there is something missing from your analysis-- or else why would Britain have joined, in the 1st place?-- and I think this applies to your thinking on Germany & France, as well (not to mention all the other nations, you bypassed); I give you credit, anyway, for at least trying to take a wide-angled view. I must disagree, however, with the impression you give that the leaders of Britain have been overly concerned with the likelihood of a pan-European, political entity. For most of European history, the feudal state model has persisted in the the enlarged, multinational form. That is to say, it has largely been every nation for itself, and wars have been frequent. Certainly, British leaders have been mindful of the military alliances of other nations, but this is no different from any other European nation (including Russia). But that Britain saw Europe, itself, as a threat, rather than just alliances of certain competing powers, which happened to be in Europe-- unsurprisingly, since that was the British Isles' part of the world-- is an inaccurately revisionist way of looking at history.

 

The British Isles are a part of Europe, of course.
Just as Ireland is also a part of the British Isles, paradoxical as it may sound.

 

Germans do not think of invading anything or anybody.
They are glad if Germany is not invaded.

 

I was just explaining that historically Britain does have some reason for not wanting to join, or does have some reason for wanting to see the union in Europe break up.
The fact they did join for a while does not necessarily mitigate what I said.

There can be reasons both for and against something, and the existence of one can weaken the other.