Why do Hindus believe in cremation instead of burial?
Earlier answerers have given a sociological explanation for the cremation ritual, but I'll try to provide a purely theological explanation.
In Hinduism, every jiva is made of five Mahabhootas, namely, Dhara (Earth), Nabh(Ether), Vayu(Air), Varuna(Water), Agni(Fire). After death, the body is supposed to disintegrate back into these many Mahabhoota.
Hindus believe that souls after living in the body for so long time, get attached to the body and if left to rot on its own or buried, will linger in the vicinity. So, burning the body makes the soul depart to its rightful place sooner than burial.
Hence, sadhus (enlightened persons) and children are not cremated, rather buried because the soul of a sadhu is already enlightened and the souls of children are not bound to the body too long to get attached to the body.
Also, Agni has a special status among the Pancha Mahabhootas (Five Elements) in being the purest of pure. All the remaining Mahabhootas become impure after they are used for cleaning. For instance, Water after being used to clean filth, itself becomes impure and cannot be used; Air after being inhaled becomes CO2 and cannot support life. Similar things hold for Earth and Ether.
Fire is the only exception. Fire, even after being used to burn and purify, remains pure and potent. Thus the concept of Agni Pareeksha, Agni Saakshi, etc.
And for this reason, Fire is used to liberate the body back to its origins in the Pancha Mahabhootas.
Also, see Hindu Funeral Rites.
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