The LED on pin 6 does not turn off. What is wrong in my sketch?

Question

Arduino

Each time a button is pressed, the LED on the corresponding pin lights up.
As soon as the counter led_counter reaches the value 9, its value is set to = 4 and each time the button is pressed
, the enabled LEDs turn off in turn, but this does not happen on pin 6.
LED state inversion is implemented by digitalWrite(led_counter, !digitalRead(led_counter)); , but for some reason the value of digitalRead(led_counter) on pin 6 when the LED is on is = 0 and when inverted it remains on.
Question for the connoisseurs. What's wrong?

boolean but1     = 0;
boolean led_flag = 0;
boolean flag     = 0;
unsigned long last_press;

byte led_counter = 4;

void setup() {
   pinMode(A5,INPUT_PULLUP);
   pinMode(4,OUTPUT);
   pinMode(5,OUTPUT);
   pinMode(6,OUTPUT);
   pinMode(7,OUTPUT);
   pinMode(8,OUTPUT);
   pinMode(9,OUTPUT);


   digitalWrite(4,0);
   digitalWrite(5,0);
   digitalWrite(6,0);
   digitalWrite(7,0);
   digitalWrite(8,0);
   digitalWrite(9,0);
   
   Serial.begin(9600);
}

void loop() {
  boolean but1 = !digitalRead(A5);
  if (but1==1 && flag==0 && millis()-last_press > 50){
    flag = !flag;
    Serial.println("Button pressed");
    last_press = millis();
  }

  if (but1==0 && flag==1){
    flag = !flag;
    //Serial.println("Button released"+ String(led_counter));
    led_flag = !led_flag;
    digitalWrite(led_counter, !digitalRead(led_counter));
    led_counter++;
    if(led_counter>9) led_counter = 4;
  }
}

Answer 1

You are trying to read the value of a pin in the OUTPUT mode.

Answer 2

digitalWrite(led_counter, !digitalRead(led_counter));
This design is somewhat controversial.
I would do this:
led = !led ;
digitalWrite ( led_counter, led );
And on each pass the state will change to the opposite.