People in the wealthier countries of the EU are thinking of leaving it, how do you think they would feel about creating an army for the whole union? Besides that, as mentioned by other people, several EU members are also members of NATO already.
Not only that, the countries within the EU all have very different backgrounds and foreign policies and will not always agree with each other, that is why it was founded mainly as a monetary union, intended to unite the countries' monetary policies.
Not only that, the countries within the EU all have very different backgrounds and foreign policies and will not always agree with each other, that is why it was founded mainly as a monetary union, intended to unite the countries' monetary policies.