It’s more convenient to think of [] as an operator for pointers rather than arrays; it’s used with both, but since arrays decay to pointers array indexing still makes sense if it’s looked at this way. So essentially it offsets, then dereferences, a pointer.
So with argv[1], what you’ve really got is *(argv + 1) expressed with more convenient syntax. This gives you the second char * in the block of memory pointed at by argv, since char * is the type argv points to, and [1] offsets argv by sizeof(char *) bytes then dereferences the result.
(*argv)[1] would dereference argv first with * to get the first pointer to char, then offset that by 1 * sizeof(char) bytes, then dereferences that to get a char. This gives the second character in the first string of the group of strings pointed at by argv, which is obviously not the same thing as argv[1].
So think of an indexed array variable as a pointer being operated on by an “offset then dereference a pointer” operator.