Srila Prabhupada speaks on the appearance of Lord Krishna-
This earth personified approached Brahmā. Bhuvārthitaḥ jātaḥ. So Brahmā prayed to the Supreme Personality of Godhead that: "This is the position of the world. So it is now overburdened with demons." So Kṛṣṇa comes:
yadā yadā hi dharmasya
glānir bhavati (bhārata)
tadātmānaṁ sṛjāmy aham
He appears. This is the process. So somebody says Kṛṣṇa appeared on the request of Brahmā when he prayed for His appearance on account of overburden, weight of the world.
So Kṛṣṇa came. And you have seen our Kṛṣṇa Book, how much He's engaged in killing the demons. In killing the demons. So Kṛṣṇa says that: "I come down, paritrāṇāya sādhūnāṁ vināśāya [Bg. 4.8], to kill the demons." So killing business is there. Kṛṣṇa. Although His killing and protecting the same thing. Because He's absolute. But the killing business is there. Therefore Kṛṣṇa has, the Nārāyaṇa has got two hands, club and disc. That is for killing the demons. And two hands, conchshell and lotus flower. That is for the devotees.
The devotees are protected. Kaunteya pratijānīhi na me bhaktaḥ praṇaśyati [Bg. 9.31]. Kṛṣṇa is bugling with His conchshell that: "My devotees will not be vanquished." And the lotus flower is the symbol of blessing. It is in the hands of Lakṣmījī also sometimes, blessing.
So somebody says that Kṛṣṇa appeared for this purpose, somebody says Kṛṣṇa appeared for this purpose, but the real conclusion is that Kṛṣṇa appeared for His own pleasure. Not, not being bound by any cause. Kṛṣṇa is fully independent. Just like we take our birth being bound by the cause of our karma. Kṛṣṇa does not come being bound up by somebody's request or by His karma. He comes out of His free will. Ātma-māyayā. It is said ātma-māyayā. He's not compelled by another's māyā. Just like we are compelled by the energy of Kṛṣṇa, external energy, this material energy. We are compelled to take birth. Kṛṣṇa does not take birth in such condition. Ātma-māyayā. Not by the... Because māyā is under the control of Kṛṣṇa. So how māyā can control Kṛṣṇa? One who thinks that Kṛṣṇa is also like us, controlled by māyā, they are called mūḍhas. Avajānanti māṁ mūḍhā mānuṣīṁ tanum āśritam
Śrīmad-Bhāgavatam 1.8.34 -- Los Angeles, April 26, 1973