Lord Kṛṣṇa is the reservoir of transcendental loving transactions with Śrīmatī Rādhārāṇī. The subject of those loving transactions is the Lord Himself, and Rādhārāṇī is the object. Thus the subject, the Lord, wanted to relish the loving mellow in the position of the object, Rādhārāṇī.
The second reason for His appearance was to understand the transcendental mellow of Himself. Lord Kṛṣṇa is all sweetness. Rādhārāṇī’s attraction for Kṛṣṇa is sublime, and to experience that attraction and understand the transcendental sweetness of Himself, He accepted the mentality of Rādhārāṇī.
The third reason that Lord Caitanya appeared was to enjoy the bliss tasted by Rādhārāṇī. The Lord thought that undoubtedly Rādhārāṇī enjoyed His company and He enjoyed the company of Rādhārāṇī, but the exchange of transcendental mellow between the spiritual couple was more pleasing to Śrīmatī Rādhārāṇī than to Śrī Kṛṣṇa. Rādhārāṇī felt more transcendental pleasure in the company of Kṛṣṇa than He could understand without taking Her position, but for Śrī Kṛṣṇa to enjoy in the position of Śrīmatī Rādhārāṇī was impossible because that position was completely foreign to Him. Kṛṣṇa is the transcendental male, and Rādhārāṇī is the transcendental female. Therefore, to know the transcendental pleasure of loving Kṛṣṇa, Lord Kṛṣṇa Himself appeared as Lord Caitanya, accepting the emotions and bodily luster of Śrīmatī Rādhārāṇī.
Lord Caitanya appeared in order to fulfill these confidential desires, and also to preach the special significance of chanting Hare Kṛṣṇa, Hare Kṛṣṇa, Kṛṣṇa Kṛṣṇa, Hare Hare/ Hare Rāma, Hare Rāma, Rāma Rāma, Hare Hare and to answer the call of Advaita Prabhu. These were secondary reasons.