Europe is quite a large area, with many different countries. I agree with Crimsonghost that cooperation is good, but creating one central military for all of these different countries would be very difficult. This unified military would not really be a show of cooperation, but instead a large body that would become inefficient. Cooperation would be separate armies working together, instead of merging to create one. This is much easier because each military would only have to deal with their country, whereas a unified military would have to deal with every country.