MY QUESTION :
See similar question and reference from Manu Smriti
Of the 8 types of marriage, the first and foremost is Brahma type, where groom's family comes searching for bride, and she is given as kanyadaan to a brahmachari who has completed gurukula and done samavartana.
It is to be done "Pradanam prak rtoh:" - Before Rtu (menses)
Marriage for girl is same as Upanayana for boy - they both have to surrender to someone at age 7 - 16 - boy surrenders to guru, girl surrenders to husband. 7 is lower limit (but not hard limit, it can be done earlier for spiritually advanced aspirants) , 16 is upper limit, according to shastras, for both upanayana & marriage. Beyond this, it loses both effectiveness and charm. There are prayaschittas for late doing too, but don't know how many people do it, or how useful it is.
Source - http://kamakoti.org/hindudharma/part18/chap5.htm , and other chapters dealing with age of marriage, and why 'progressive' thinkers tried to increase age of marriage, and how Britishers passed law to enact Sarda act even though opinion among people was split 50-50.
Even on this site, 'forward' thinkers are going to post comments arguing against this saying it goes against 'Constitution', which was a document copied from constitutions of various countries, written within past 100 years, in mlechha basha, with little consideration for Bharatha Kalachaar and her ancient Dharma Shastras.
As I mentioned in a comment above, Child marriage does not mean child-physical relations (aka pedophilia). The girl is only sent to husband's home after puberty. Also this is not like modern day 'grooming' where the sole purpose of older men is lust.
You have to build a protective wall around the heart before lust enters it, that is the reason for doing upanayana and marriage before puberty. But nowadays most people don't follow this - boys get upanayana at age 24 and girls marry at age 24.
You can clearly see lustful consequences in society today of not following both above practices.
What's the true (scriptural) reason behind Child Marriage?
TL;DR: For the same reason a child is admitted to school at a very early age and not at age 20. For the Hindu woman, husband is the ultimate God (Pati Parameshwar). So why not get to know him and his family (in-laws) from an early age – this seems to be the basic idea.
In the book Hindu Dharma: The Universal Way of Life by Swami Chandrasekarendra Saraswati, there's a whole chapter on this very topic so I'm only quoting below a few relevant lines.
A girl must become attached to her husband [that is she must be married] before her mind is distributed by thoughts of love and desire and before she begins to take an interest in her body. The innocent child that she is now, she will have the humility to regard her husband in an attitude of surrender in the thoughts that he alone is her guru and that he alone is her Isvara.
Women in Andhra Pradesh and Maharashtra even today observe many vratas. Unmarried girls in these parts of the country worship Siva, looking upon him as their husband. When they get married they worship the husband as Siva. First a girl, before her marriage, worships Siva as her husband; later whoever comes into her life as her husband she looks upon as Siva.
In childhood a girl does not ask questions. It is now that she will, out of her simple faith, look upon her husband as Paramesvara. This faith, formed in her innocence, will take firm root in her mind when she becomes older and begins to understand things.
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According to the Dharmasastra, a girl must be entrusted in the hands of a man, that is her husband, before she starts feeling the urge of kama. She will then become steeped in the belief that he is her Lord. And when she begins to feel the natural urges she will dedicate her body to him. This is the law of the Dharmasastra.
[ Hindu Dharma » Marriage » Why Child Marriage ]
One main reason of child marriages is to prevent dating, premarital sex, promiscuity, and having multiple partners.
Adolescents and teens, who don't follow the rules of Brahmacharya, are known to be very passionate and long for love and sex. Just take a look at the West, kids start having sex and dating by the time they are 12 years old and then have multiple relations. This is quite a normal thing. So, to prevent these immoral activities, because it is natural, and because most women wouldn't follow the rules of Brahmacharya, parents would get their girls married right before puberty.
In the event that parents don't marry the daughter within 3 years of the onset of menstruation, the Shastra says that the girl is allowed to marry any man of equal caste she chooses and doesn't incur sin for doing so.
