My history teacher once told us that aides to Joseph Stalin had warned him about messing too much with the Catholic Church.
Stalin in return asked the (rethorical) question: "And how many divisions does the Vatican have?".

So, the reason the EU wants its own army is that without an army, you're not taken seriously.

The reality is, of course, that nobody takes the EU for serious, regardless - not having its own army isn't the key-reason for that.

And the army would probably (and on purpose) be weaker than even the army of the weakest of its member states....