Why do hindus believe in reincarnation?

AnswerIn Hinduism there is a difference between the inner soul and outer body. The inner soul is the real person and outer body is only a container.

One classic story explaining the duality ... A master asks his student "what is that?" pointing to something he is holding in his hand - the student answers "My pen". Master says "Ok - you say so because that belongs to YOU." then the master asks "What is holding the pen?" Sudent answers "My hand" Master goes on - "What makes you think? " Student-"My brain", Master- "What makes you live?" Student-"My Heart" . Finally master says - "Like the Pen you treat all the others as something which belongs to you - what is that YOU". The student has no answer.

Hinduism calls that YOU as the ATHMA - the inner soul. All other things including the body is just outside YOU. Hindus believe that the soul is separate from the body and it will reincarnate when the body is no more able to live in this world. The soul will rest or join the ultimate soul (PARAM-ATHMA) when it is ready to leave itself. It is believed the soul is ready when it has relieved itself of all earthly pleasures - which are all induced by this body (love, pain, hurt, ego, sex etc).

Aupmanyav adds: My friend here has given you the religious take. I am an atheist hindu. Here is my take on reincarnation:

It was a strategy to make people engage in good deeds because they got you better next birth. At the same time, it discouraged people from engaging in evil deeds as they could be reincarnated as worms. It was a social strategy.
Reincarnation is spiritually believed since it is mentioned in religious scriptures. Law of conservation states that some thing can not be reduced to nothing.