Rotate Around a character World X axis - weird issue

Hello, I'm trying to get the main camera to rotate around the main character in two possible axis: Y and X. Both of them are archieved by the RotateAround() method:

 using UnityEngine;
 using System.Collections;
 
 public class world_camera : MonoBehaviour {
 
     GameObject MC;
     Vector3 MCInitPos, MCFinPos, cameraMCPos;
     public float turnSpeed, thetaAngle;
 
     // Use this for initialization
     void Start () {
 
         MC = GameObject.FindWithTag("Player");
         MCInitPos = MC.transform.position;
         turnSpeed = 20.0F;
         gameObject.transform.LookAt(MC.transform.position);
     
     }
     
     // Update is called once per frame
     void Update () {
 
 
         MC = GameObject.FindWithTag("Player");
         MCFinPos = MC.transform.position; 
 
         cameraMCPos = gameObject.transform.position - MCFinPos;
         thetaAngle = Mathf.Acos(cameraMCPos.y/cameraMCPos.magnitude);
 
         if(Input.GetKey(KeyCode.LeftArrow)){            
             gameObject.transform.RotateAround(MC.transform.position,Vector3.up,turnSpeed*Time.deltaTime);
         }
         else if(Input.GetKey(KeyCode.RightArrow)){
             gameObject.transform.RotateAround(MC.transform.position,Vector3.up,-turnSpeed*Time.deltaTime);
         }
         else if(Input.GetKey(KeyCode.UpArrow)){
             if(thetaAngle>(0.0F+0.02F)){
                 gameObject.transform.RotateAround(MC.transform.position,Vector3.right,turnSpeed*Time.deltaTime);}
         }
         else if(Input.GetKey(KeyCode.DownArrow)){
             if(thetaAngle<(Mathf.PI/2-0.02F)){
                 gameObject.transform.RotateAround(MC.transform.position,Vector3.right,-turnSpeed*Time.deltaTime);}
         }
 
         else if(Input.GetKey(KeyCode.Keypad0)){
             gameObject.transform.Translate(Vector3.forward*turnSpeed*Time.deltaTime);
         }
 
         else if(Input.GetKey(KeyCode.KeypadPeriod)){
             gameObject.transform.Translate(-Vector3.forward*turnSpeed*Time.deltaTime);
         }
 
         gameObject.transform.LookAt(MC.transform.position);
         gameObject.transform.position+=new Vector3((MCFinPos-MCInitPos).x,0,(MCFinPos-MCInitPos).z);
         MCInitPos = MC.transform.position; 
 

The thing is: the Y-axis rotation works fine: it rotates around the main character, but the X-axis rotation is weird, since it performs a rotation around the X-axis, not OVER the main character, but a bit displaced.

It is just like the rotation is performed in another plane that doesn't cross the main character, as it should be if I want an X-rotation over it.

Have you got any thoughts about why is this?

Thank you very much in advance.