This a summary and compilation of what Dr Naik mentioned in his video concerning Aisha's age of marriage, with several respected, scholarly sources to back up what he is saying.
1. The hadeeth concerning the marriage of Aisha (may God be pleased with her) and its consummation from 'Bukhari' is considered authentic.
2. Dr Naik is a medical doctor. He was taught that: the age at which a female reaches maturity changes depending on several, interdependent factors including diet and nutrition, climate, environment. Modern science tells us that the age of puberty is earlier closer to the equator. An additional point here: Females tend to mature earlier than males.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2465479/ Adults at 12? Trends in puberty and their public health consequences
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6378593/ Timing of puberty in boys and girls: A population‐based study
en.wikipedia.org
Human Sexuality and its Problems (2008), John Bancroft - Page 191
Clinical Gynaecology (2007), Kruger, Bother et al. - Page 287
View attachment 36184 From 'Human Sexuality and its Problems'
3. Today, whether in India (where Dr Naik is from), or in America, it is normal for a girl to achieve the age of puberty (the beginning of the menstrual cycle) at age 12, 13 or 14. Moreover, it is normal that a girl might reach the age of puberty at age 9 or 10. If the age of menstruation occurs before the age of 9, this is an indication that she may have a developmental disorder, e.g. 'precocious puberty'.
4. Islam dictates that when a female and male reach puberty, they are eligible for marriage. (Scientifically, when a female reaches the age of puberty, she is capable of reproducing, and giving birth to a living, fertile offspring.)
5. Every country has its own laws. In India, a girl can only marry at the age of 18. In America, the age of marriage is 16.
6. As such, if a couple were to be married at age 16, it would be illegal in India, but legal in America. What is legal in America may be illegal in India, and what is illegal in America may be legal in India.
7. In the state of Texas, it is customary to marry early. It is acceptable there, because it has been their historic custom for generations. In Massachusetts "the traditional minimum common law marriageable age of 12 for girls and 14 for boys may still be in effect" (source:
https://en.wikipedia.org/wiki/Marriage_age_in_the_United_States).
8. Thus, what we realise is that everyone has their own criteria. As far as Islam is concerned once a girl or boy reaches the age of sexual maturity, they are permitted to marry.
9. Aisha (may God be pleased with her) was unique.
She was the exception, not the rule. Likewise, the immaculate conception of the Virgin Mary, who may only have 13 or 14 herself, is
the exception and not the rule.
10. When we read about the life of Aisha, she was very mature and intelligent: We know that she narrated many of the sayings of the Prophet Muhammad, which were compiled in books of hadeeth. Aisha is in fact credited with being one of the leading narrators of the words and actions of the Prophet, along with Abu Hurairah, another companion of the Prophet.
11. We know that after Aisha was married to the Prophet Muhammad, he only went on to live for 10 years. Had she married after the age that she had, she wouldn't have been able to narrate all the hadeeth she had narrated while the Prophet was living.
I hope that this answers all your questions.