Why did Swami Vivekananda preach Advaita to his disciples?

[An online spiritual discussion was conducted on February 20, 2021, in which several devotees participated. Some of the questions of devotees answered by Swāmi are given below.]

[Śrī Veerabhadra Sastry asked: In one context, Śaṅkarācārya said “Ahaṃ Brahmāsmi” and His disciples repeated the same. So, Śaṅkarācārya drank some molten metal, which His disciples could not. So, He proved that He was God and was different from all souls. In the Bhagavad Gītā, it is said as follows:

Anekabāhūdara vaktra netraṃ paśyāmi tvāṃ sarvato’nantarūpam|

Nāntaṃ na madhyaṃ na punastavādiṃ paśyāmi viśveśvara viśvarūpa||

When Swami Vivekananda’s disciples were weeping, he said the following words to them:

kiṃ nāma rodiṣi sakhe tvayi sarvaśaktiḥ

āmantrayasva bhagavan bhagadaṃ svarupam|

trailokyametadakhilaṃ tava pādamūle

ātmaiva hi prabhavate na jaḍaḥ kadācit ||

Here Swami Vivekananda said that all souls are Incarnations, even though at present we may be ignorant. My question is, whether Swami Vivekananda said so only to motivate his disciples and fill them with optimism? Why did he say to his disciples that the three worlds are at your feet?]

Swāmi replied: The reason for Śaṅkara saying that every soul is God was to turn atheists into theists using a three step formula. He said (1) “You are God”, (2) “You exist” and (3) “Therefore, God exists”. The reason for Śaṅkara drinking the molten lead was to preach to His the already-theistic devotees to follow dualism and worship God like servants. The reason for Swami Vivekananda saying the above to his disciples was to give courage and confidence to them. He wanted the youths to do good work and give up fear. The preaching given by a divine preacher in one context should not be mixed with that given in another context. Every preaching is correct because it is as per the needs of the context.