Also, the EU isn't even remotely like "a country".
The EU has a currency, parliament, elections, laws, presidents, courts, treaties, and is thinking about forming an army. That sounds an awful lot like a country to me.
In practice, being a country isn't just about filling out some checklist. The EU neither claims to be a country, nor does any country on Earth see it as a single sovereign state. It has democratic and political processes that are similar to a country's, but its sway over member states is limited. Also, its members aren't forced to stay in the EU, unlike the individual regions that are part of your country.
And if you truly, unironically believe that the EU is a single country, what do you think of its member states? By extension of this argument, is Spain not a country? Or is Poland a country that's contained within another country, being equal and unequal in status at the same time?
If it looks like a duck, swims like a duck, and quacks like a duck, it still might not be a duck.