To explain it another way: The way the game is currently designed, the Fighter class represents a general concept, and then through a combination of background, theme, and class feature choices, you can choose what specific kind of fighter you want to be.
I think that is where the problem starts. The fighter is a general concept. It is not the general warrior.
The fighter (for several editions) is an expertly trained warrior, is very comfortable all sorts of armor, and has some sort of mastery of several weapons based martial arts.
The Ranger, Paladin, and Barbarian aesthetically feel like "specific kinds of fighter," so the aesthetics of the design would have them as backgrounds, themes, and/or class feature choices. The problem is, for a variety of reasons (summarized below), some of them can't fit into those slots (though some of them can, and should). Therefore, if they are separate classes, I feel it would be best to describe those classes explicitly as being "specific kinds of fighter."
With the above definition, Ranger, Paladin, and Barbarian are not "specific kinds of fighter". They are special kinds of warrior.
The Ranger is a warrior of necessity. He walks the parts of the world where combat is unavoidable as he is either protecting an area, defending himself or allies, or is actively hunting hostile prey. The only thing a ranger and fighter have in common is that they use weapons and are good at using them.
The Barbarian is warrior of instinct and emotion. Many are not formally trained and substitute rage and fury for technique. The only thing a barbarian and fighter have in common is that they use weapons and are good at using them.
etc etc.
So unless all you define a fighter as is someone who "use weapons and are good at using them", the other classes are not special types of fighter.