The hunter eagle (Indra) wanted the pigeon (Agni) back from the King (Sibi). The King wanted to give it some other meat to eat and requested the bird not to kill the pigeon. The hunter bird refused to accept the King's offer
SB Canto 1
This child will be a munificent donor of charity and protector of the surrendered, like the famous King Śibi of the Uśīnara country. And he will expand the name and fame of his family like Bharata, the son of Mahārāja Duṣyanta.
A king becomes famous by his acts of charity, performances of yajñas, protection of the surrendered, etc. A kṣatriya king is proud to give protection to the surrendered souls. This attitude of a king is called īśvara-bhava, or factual power to give protection in a righteous cause. In the Bhagavad-gītā the Lord instructs living beings to surrender unto Him, and He promises all protection. The Lord is all-powerful and true to His word, and therefore He never fails to give protection to His different devotees. The king, being the representative of the Lord, must possess this attitude of giving protection to the surrendered souls at all risk. Mahārāja Śibi, the King of Uśīnara, was an intimate friend of Mahārāja Yayāti, who was able to reach the heavenly planets along with Mahārāja Śibi. Mahārāja Śibi was aware of the heavenly planet where he was to be transferred after his death, and the description of this heavenly planet is given in the Mahābhārata (Ādi-parva 96.6-9). Mahārāja Śibi was so charitably disposed that he wanted to give over his acquired position in the heavenly kingdom to Yayāti, but he did not accept it. Yayāti went to the heavenly planet along with great ṛṣis like Aṣṭaka and others. On inquiry from the ṛṣis, Yayāti gave an account of Śibi's pious acts when all of them were on the path to heaven. He has become a member of the assembly of Yamarāja, who has become his worshipful deity. As confirmed in the Bhagavad-gītā, the worshiper of the demigods goes to the planets of the demigods (yānti deva-vratā devān (BG 9.25)); so Mahārāja Śibi has become an associate of the great Vaiṣṇava authority Yamarāja on that particular planet. While he was on the earth he became very famous as a protector of surrendered souls and a donor of charities. The King of heaven once took the shape of a pigeon-hunter bird (eagle), and Agni, the fire-god, took the shape of a pigeon. The pigeon, while being chased by the eagle, took shelter on the lap of Mahārāja Śibi, and the hunter eagle wanted the pigeon back from the King. The King wanted to give it some other meat to eat and requested the bird not to kill the pigeon. The hunter bird refused to accept the King's offer, but it was settled later on that the eagle would accept flesh from the body of the King of the pigeon's equivalent weight. The King began to cut flesh from his body to weigh in the balance equivalent to the weight of the pigeon, but the mystic pigeon always remained heavier. The King then put himself on the balance to equate with the pigeon, and the demigods were pleased with him. The King of heaven and the fire-god disclosed their identity, and the King was blessed by them. Devarṣi Nārada also glorified Mahārāja Śibi for his great achievements, specifically in charity and protection. Mahārāja Śibi sacrificed his own son for the satisfaction of human beings in his kingdom. And thus child Parīkṣit was to become a second Śibi in charity and protection.
Dauṣyanti Bharata: There are many Bharatas in history, of which Bharata the brother of Lord Rāma, Bharata the son of King Ṛṣabha, and Bharata the son of Mahārāja Duṣyanta are very famous. And all these Bharatas are historically known to the universe. This earth planet is known as Bhārata, or Bhārata-varṣa, due to King Bharata the son of Ṛṣabha, but according to some this land is known as Bhārata due to the reign of the son of Duṣyanta. So far as we are convinced, this land's name Bhārata-varṣa was established from the reign of Bharata the son of King Ṛṣabha. Before him the land was known as Ilāvati-varṣa, but just after the coronation of Bharata, the son of Ṛṣabha, this land became famous as Bhārata-varṣa.
But despite all this, Bharata, the son of Mahārāja Duṣyanta was not less important. He is the son of the famous beauty Śakuntalā. Mahārāja Duṣyanta fell in love with Śakuntalā in the forest, and Bharata was conceived. After that, Mahārāja forgot his wife Śakuntalā by the curse of Kaṇva Muni, and the child Bharata was brought up in the forest by his mother. Even in his childhood he was so powerful that he challenged the lions and elephants in the forest and would fight with them as little children play with cats and dogs. Because of the boy's becoming so strong, more than the so-called modern Tarzan, the ṛṣis in the forest called him Sarvadaman, or one who is able to control everyone. A full description of Mahārāja Bharata is given in the Mahābhārata, Ādi-parva. The Pāṇḍavas, or the Kurus, are sometimes addressed as Bhārata due to being born in the dynasty of the famous Mahārāja Bharata, the son of King Duṣyanta.