Why does Pi apologize to Richard Parker for failing as a trainer?

Pi apologizes to Richard Parker for failing as a trainer because he feels a deep sense of responsibility for the tiger's well-being and their shared survival. He recognizes that he hasn't effectively established dominance or trust, which are crucial for their coexistence. This acknowledgment reflects Pi's emotional turmoil and his desire to maintain a bond with Richard Parker, seeing him not just as a threat but as a companion in their dire circumstances. Ultimately, Pi's apology highlights the complexity of their relationship in the struggle for survival.