I don't see a argument in having separate armys.

The main argument is that a european army would have to be overseen by some european institution like the EU Parliament or the Commission. That institution would decide whether or not Germans, French, Czech and so on would have to go to war or not. A scenario is possible where say Germany and Poland are opposed to a mission carried out by the EU Army but are outvoted and hence have to send their people into something they deem is wrong.

I for one see no majority in Germany to give up sovereignty in that matter to the EU. I´m glad that the Bundestag, i.e. the german parliament, and the Bundestag only decides whether or not we send our soldiers to war. European nations have differing degrees of inclination to the use of force and that should be reflected in the general political outcome.

That being said, Europe has a lot of potential in regards of joint R&D in defense, in pooling of purchases of military equipment, joint units and exercises and so on. We should rather focus on working better together and making each member stronger rather than giving up sovereignty to some far away EU institution that´s supposedly will make wise decisions for some 500 million people.