Why must I inquire into my own self? The reason is because you have taken your self to be an entity that is limited to the body and mind. An entity that is born and will die. An entity that assumes ownership of actions. An entity that believes itself to be the do-er of actions. An entity that believes it has feelings and emotions. An entity that believes that the present is not good enough and that someday or sometime in the future, it will achieve a state of peace or happiness or some state better than the present. An entity that hopes for a better day. An entity that is suffering and pining for a better mental state.
As long as there is a BELIEF in this entity, which you call 'me' or 'I' (the first person) there will no doubt be suffering. The false belief in this self centered entity is the cause of all suffering.
There are essentially two main ways in which this false belief can come crumbling down. One, is the sincere and complete faith and belief in the sayings of the Sages or the Guru. The Sages have repeatedly said over the ages that "the REAL YOU are not the body nor the mind". With sheer devotion to your Guru or the Sage, and if the mind is pure enough, just this LISTENING is enough and the false 'I' will immediately vanish. However, for the majority of seekers, due to years and years of mental conditioning and the strong belief in an entity called 'me', many questions persist which prevent him/her from executing the sheer devotion needed to accept the Guru's sayings. In such cases, where the belief in the entity 'me' is very strong, it becomes necessary to investigate, inquire, as to who is this 'me'. This investigation or inquiry by a 'me' into the nature of 'me' is called Self-inquiry (or Self-enquiry if you are British or from the Commonwealth!). With this inquiry, all one is doing is convincing oneself that there is really no-thing or no-one or no-entity called 'me'. It is all just a thought. It is the prime thought or the root thought (the 'I-thought') to which all other thoughts are attached. On proving the falseness of this prime thought (the 'I-thought' or the 'me') the other thoughts have nothing to hold on to and they gradually fall away, leaving only the PURE BEING to shine through effortlessly.