Why a group is called allies in war?

In WWI I see that we have Central Powers and Allies. Both are groups of countries who fight together against the other group.

In WWII we again have Allies and Axis.

I can't understand why do we call a group allies, while both groups are composed of allies.

I can understand it deductively if we call one group Attackers and the other Defenders. But Allies always puzzles me and I need to check to ensure which group is called what.

What is the reason behind this wrong naming?

This is another manifestation of the same word functioning as a common noun when it is not capitalised, and as a proper name, standing for something more specific, in its capitalised form. Many religious institutions aspire to be catholic (with lowercase c), but Catholic (capitalised) stands for only one of them. In the United States, the supporters of one particular party are Democrats (capitalised), but many more people are democrats (lowercase), in that they generally support democracy. In the same way, any group of countries that are fighting together, on the same side, in a war (or, more broadly, people/organisations that are fighting on the same side of any conflict) can be called allies (lowercase), but only some particular such groupings named themselves Allies (capitalised). Of course, in a context in which the audience expects such a term to be used in its proper-name sense, it is wise to avoid using it in its common-noun sense.

The British, being native speakers of English, got to determine what each side of the war was called in English, and in both cases, they chose the term “Allies” for their own side, presumably short for “Britain and its allies”. There was no reason for the Americans, also native speakers, to not go along with that. And the French weren’t in a position to argue with the powers coming to save them (again).

The Germans, Italians, Japanese, etc. presumably picked names in their languages that were presumably more flattering to their sides.