Here are some reasons why in the flag of EU the number of stars did not become 15 when the States became 15.

The 12 stars do not represent 12 countries, but rather 12 as some kind of representation of perfection / unity. I think one cannot make comparisons with the US flag as the cultural and historical environment is very different (and flags do reflect these conditions).As everyone knows the flag of the Council of Europe is the same, blue with twelve stars, and its members are a lot more than 12.

US add a star in the canton for each new state, and added a new stripe for each of the first two new states, Vermont and Kentucky. The US flag had fifteen stars and fifteen stripes from 1795 to 1818. When it became clear that the nation would continue to grow, the stripes were reduced to the original thirteen, but the stars continued to multiply.

From The Otago Daily Times (NZ) on Monday Jan. 9th 1995
« No need to Change the Flag » (by Roberyt J. Wielaard)

It adorns car licence plates in some of the 12 European Union nations and greets travellers at border points from Athens to Amsterdam to the Azores. But 40 years after it was created, the European flag and its twelve gold stars on a field of blue remain a source of confusion. Contrary to popular belief, its stars do not represent the current 12 members of the European Union. So, with Austria, Finland and Sweden joining the EU this month, not a single star will be added to the European flag.

The European flag was designed after a five-year squabble, starting in 1950. Bureaucrats studied more than 100 designs - rings, crosses, stars, suns, triangles - sent in by artists, heraldry experts and Euro-enthusiasts. In 1953, a circle of stars was put on a short list by the Council of Europe (the first post-war organisation for European integration). Two more years were needed to pick a blue background. The Council had 15 members in 1955, but Germany (FRG) vetoed 15 stars since one was for the Saarland region, then under French control. It wanted 14 stars, but France disagreed because it excluded Saarland, which did not rejoin Germany until 1957. No-one liked the superstitious number 13, but 12 was found to hold great Judeo-Christian symbolism (through the 12 tribes and 12 apostles). Also, in Greek mythology, Hercules gained immortality through 12 labours. By 1957 the Council of Europe had 25 members. The more powerful organization (EU or European Union, as it is now known), founded that year by six nations, now has 15 members. A dozen more is waiting in the wings.

The difficulty in picking a European flag was not an isolated bout of ambivalence over Euro-symbols. The Council of Europe spent eight years selecting a European anthem. In 1972 it picked Ode to Joy from Beethoven's Symphony no. 9, which has since been adopted by the EU. In the 1980s, the EU spent seven years arguing over the colour of the European passport, eventually picking "Bishop Red". Ironically, this does not show the European flag or its 12-star logo, but the national emblems of each issuing nation. The European nations have also had trouble choosing a common holiday, so now there are two: May 5 and May 9. The Council of Europe uses the former because on that date in 1949 Britain's Sir Winston Churchill declared in a speech in Zurich : « We must build a United States of Europe ». The EU calls May 9 Robert Schuman Day in honour of the French statesman who was a key founder of the union.