Rotation around player is broken, does rotateAround not work correctly in 2D?

Question

I'm making a Geometry Wars style game. I'm programming an enemy to move towards the player and start rotating around the player when the enemy is close enough. However, with my current code the enemy rotates in a triangle around a point in front of the player. Any idea what's causing it?

 {
     public Transform player;
     public Rigidbody2D rb;
     public float enemySpd = 3;
 
     void Start()
     {
         //Sets player to the transform of the player
         player = GameObject.FindGameObjectWithTag("Player").transform;
     }
 
 
     void FixedUpdate()
     {
         FollowPlayer();
     }
 
     void FollowPlayer()
     {
         //Moves the enemy towards the player
         transform.right = player.position - transform.position;
         //Gets the distance between the enemy and the player
         float dist = Vector2.Distance(player.position, transform.position);
         //Sets zAxis to the z axis for the enemy to rotate around
         Vector3 zAxis = new Vector3(0,0,1);
         //Sets vec to an X axis for the directions of the enemy to face
         Vector2 vec = new Vector2(1, 0);
 
         //If the enemy is far enough away have him move toward the player
         if (dist > 3)
         {
             //Moves the enemy forward
             rb.velocity = transform.TransformDirection(vec * enemySpd);
         }
         //If the enemy is close enough stop moving forward and rotate around the player
         else
         {
             //Rotates around the Z axis of the player
             transform.RotateAround(player.position, zAxis, 1);
         }
         
 
     }
 }

Answer 1

Hello. I changed the code a little. I hope this helps :

     private Transform player;
     private Rigidbody2D rb;
 
     private void Start()
     {
         // Get components
         player = GameObject.FindGameObjectWithTag("Player").transform;
         rb = GetComponent<Rigidbody2D>();
     }
 
     private void FixedUpdate()
     {
         FollowPlayer();
     }
 
     private void FollowPlayer()
     {
         if (player)
         {
             // Moves the enemy towards the player
             transform.right = player.position - transform.position;
 
             // Gets the distance between the enemy and the player
             float dist = Vector2.Distance(player.position, transform.position);
 
             // Sets zAxis to the z axis for the enemy to rotate around
             Vector3 zAxis = new Vector3(0, 0, 1);
 
             // Sets vec to an X axis for the directions of the enemy to face
             Vector2 vec = new Vector2(1, 0);
 
             if (dist > 3)
             {
                 // If the enemy is far enough away have him move toward the player
                 rb.bodyType = RigidbodyType2D.Dynamic;
                 rb.velocity = transform.TransformDirection(vec * moveSpeed);
             }
             else
             {
                 // If the enemy is close enough stop moving forward and rotate around the player
                 rb.bodyType = RigidbodyType2D.Static;
                 transform.RotateAround(player.position, zAxis, 1);
             }
         }
     }

Rotation around player is broken, does rotateAround not work correctly in 2D?

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