Why is “while ( !feof (file) )” always wrong?

Question

I've seen people trying to read files like this in a lot of posts lately.

Code

#include <stdio.h>
#include <stdlib.h>

int main(int argc, char **argv)
{
    char *path = argc > 1 ? argv[1] : "input.txt";

    FILE *fp = fopen(path, "r");
    if( fp == NULL ) {
        perror(path);
        return EXIT_FAILURE;
    }

    while( !feof(fp) ) {  /* THIS IS WRONG */
        /* Read and process data from file… */
    }
    if( fclose(fp) == 0 ) {
        return EXIT_SUCCESS;
    } else {
        perror(path);
        return EXIT_FAILURE;
    }
}

What is wrong with this loop?