Then what you said was exactly fucking wrong.
Peter Parker is currently Spider-Man. Miles Morales is also curently Spider-Man. Otto Octavius has been Spider-Man. Ben Reilly has been Spider-Man.
Tony Stark is Iron Man. James Rhodes was also Iron Man. Victor Von Doom was Iron man. The Avengers once went back in time to bring a Teen Tony Stark into the present and he was Iron Man.
Steve Rogers is Captain America. John Walker has also been Captain America. Bucky Barnes has also been Captain America. Sam Wilson has also been Captain America.
The identities of Daredevil, Thor, Ghostrider, Captain Marvel, Wolverine, and many others have all been assumed by other characters.
It has always been this way.
It's not just Marvel either:
Multiple different characters have all taken up the mantle of Batman, Superman, Wonder Woman, etc.
Super Hero identities are not exclusively tied to one character. They are mantles that can be passed along to others.