OnTriggerEnter2D working but OnTriggerExit2D never called

My code looks like this :

     private bool itemTrigger;
     private GameObject triggerOther;
     
     private void Update () {
 
         if (!GameManager.instance.playersTurn)
             return;
         
         int horizontal = 0;
         int vertical = 0;
         horizontal = (int)(Input.GetAxisRaw ("Horizontal"));
         vertical = (int)(Input.GetAxisRaw ("Vertical"));
 
         if (horizontal != 0) 
         {
             vertical = 0;
         }
         if (horizontal != 0 || vertical != 0) 
         {
             AttemptMove<Block> (horizontal, vertical);
         }
 
         if (Input.GetKeyDown(KeyCode.E))
         {
                   if (itemTrigger == true)
         {

             if (inventory.AddItem(triggerOther.GetComponent<ItemScript>()))
             { triggerOther.gameObject.SetActive(false); }
         
         }

         }
 
     }
     
         private void OnTriggerEnter2D (Collider2D other)
     {
         if (other.tag == "Item")
         {
             Debug.Log("Enter");
             triggerOther = other.gameObject;
             itemTrigger = true;
         }
     }
     
         private void OnTriggerExit2D(Collider2D other)
     {
         if (other.tag == "Item")
         {
             Debug.Log("Exit");
             itemTrigger = false;
         }
     }

When standing on an item, I can pick it up by pressing "E"... But OnTriggerExit is never called so even if I leave my item collider, i can still pick it up...

My game is based on the Rogue-like tutorial so my MovingObjects script looks like this

     public float moveTime = 0.5f;
     public LayerMask blockingLayer;
     private BoxCollider2D boxCollider;
     private Rigidbody2D rb2D;
     private float inverseMoveTime;
 
     // Use this for initialization
     protected virtual void Start () 
     {
     boxCollider = GetComponent <BoxCollider2D> ();
         rb2D = GetComponent <Rigidbody2D> ();
         inverseMoveTime = 1f / moveTime;
     }
 
     protected bool Move (int xDir, int yDir, out RaycastHit2D hit)
     {
         Vector2 start = transform.position;
         Vector2 end = start + new Vector2 (xDir, yDir);
         boxCollider.enabled = false;
         hit = Physics2D.Linecast(start, end, blockingLayer);
         boxCollider.enabled = true;
 
         if (hit.transform == null)
         {
             StartCoroutine(SmoothMovement(end));
             return true;
         }
         return false;
 
     }
 
     protected IEnumerator SmoothMovement (Vector3 end)
     {
         float sqrRemainingDistance = (transform.position = end).sqrMagnitude;
             while (sqrRemainingDistance > float.Epsilon)
         {
             Vector3 newPosition = Vector3.MoveTowards (rb2D.position, end, inverseMoveTime * Time.deltaTime);
             rb2D.MovePosition (newPosition);
             sqrRemainingDistance = (transform.position - end).sqrMagnitude;
             yield return null;
         }
     }
 
     protected virtual void AttemptMove <T> (int xDir, int yDir)
         where T : Component
     {
         RaycastHit2D hit;
         bool canMove = Move (xDir, yDir, out hit);
         if (hit.transform == null)
             return;
         T hitComponent = hit.transform.GetComponent<T>();
         if (!canMove && hitComponent != null)
         {
             OnCantMove (hitComponent);
         }
     }
 
     protected abstract void OnCantMove <T> (T component)
         where T : Component; 
 }