Srila Prabhupada speaks on the objective of varnasrama
Srila Prabhupada : "By practice. We are training them to practice how to become devotees. By superficial seeing the activities of Krishna, this is not... One has to practice. Just like we are going to start…Gurukula means practice. ―Brahmacari guru-kule vasan dantah” [SB 7.12.1]. How to become self-controlled, danta.That is the... So our mission is to awaken the original consciousness, and that can be done by practice. Without practice, it is not possible."
Morning Walk - 14 August, 1976, Bombay
"Simply follow the program of the elders, let the children associate as much as possible with the routine KC program, and when the others go out for working and business matters, the children can be given classes as you describe. They can learn our method of Kṛṣṇa Consciousness by rising early, cleansing, plus knowledge of Sanskrit, English, a little Mathematics, history,geography."
Letter to Aniruddha - Calcutta, 7 March, 1972
Srila Prabhupada : "So therefore it is our little attempt that to train some boys to become first-class character. Samo damo titiksa. That is required in the society. Simply all fourth-class, fifth-class men, how the society will improve? That is not possible…
Without sense control nobody can make any progress in human life. Tapasya. That is called tapasya. The yoga is also another tapasya. Tapo. Tapasa brahmacaryena [SB 6.1.13]. So any path you take, the brahmacarya first thing. Without brahmacarya there is no question of tapasya."
Lecture on Srimad-Bhagavatam 5.5.18 - Vrindavana, November 6, 1976
"They may be certain their children will get the real knowledge which will create best citizens of brahminical type, clean, honest, law-abiding, healthy, industrious, all good qualities they will have."
Letter to Mohanananda, Ahembdabad, 11 December, 1972
Comments by Prabhupādanuga devotees of BIG & BIVC
"So real education, training is to make the child self controlled, celibate, obedient – overall a good devotee of Kṛṣṇa. We at BIG & BIVC are dedicated to train the child so that he develops all these good qualities and becomes a devotee of Kṛṣṇa by following Srila Prabhupāda‟s instructions of rising early in the morning, attending mangala arti, chanting, reciting shlokas, taking bath at least twice, obedient to parents, elders, guru and Kṛṣṇa etc."
"As we can see from the above quotes the main aim of gurukula is to train the child to control the mind, control the senses, observe celibacy, to become peaceful, sober, detached from so called society, friendship, love and become attached to serving Kṛṣṇa as per the instructions given by our spiritual master, Srila Prabhupāda."
For more details, please refer to Q.No.3 in the Magazine - Back to Srila Prabhupada's Gurukula