I mean i know in the past we have had wars over kings/religion/other pointless crap but in recent years i would say we are getting a long pretty well. In terms of why we always seem to be at each others throats at least politically i think it is largely to do with the fact that Europe is a pretty small continent that has basically created the world as we know it today, as a result there is a lot of pride among European people regarding their history and accomplishments which many view as devalued especially in the eyes of other European countries when talking about Europe as a whole. It's very easy to form a state when its effectively one powerful "area" absorbing lots of less powerful areas but when you have a small continent consisting of 51 countries all of which have unique and impressive elements and achievements that their citizens take pride in unifying them in a manner that the majority of the population of each country find acceptable is very very hard if not impossible.
There are other factors as well such as we don't really need to get on, both the UK and France are nuclear powers with Germany, Italy and probably a bunch others at this point all having access to nukes under US control. the UK, France and Germany all have extremely well trained and capable armies (in fact in terms of a global comparison i would argue that nearly every European country has a formidable military). Economically we aren't great but realistically we aren't that bad either, In my opinion the EU has the best human rights in the world and we have a pretty decent attitude towards education and in general are extremely progressive.
It's not so much we don't want to come together it's more there is really no need for us to at this moment in time, if there was some big global threat like Russia and China decided to merge into one super douche nation and the US sank or something the concept of merging into one big European super power would, i think, be much more likely to happen.