The question should have been not ‘is masturbation a sin in Hinduism’ but ‘why masturbation is not a sin in Hinduism?’ Sex is not considered sin in Hindu religion. But sex without consent is Adharma and it leads to total annihilation. Masturbation is widely mentioned in Hindu Puranas and Epics though not directly.
Have a balanced approach to every aspect of life. This is what is required.
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Stories of saints, rishis, who have lost control of their will power and resulting in their semen falling out is found throughout Puranas. The villain in most cases is Indra, the king of Demigods. He gets the service of Apsaras or heavenly maidens for the purpose.
There are also stories of women who have amorous feelings for men and them getting lost in their thoughts. Here too masturbation is not directly mentioned but we can read it between the lines.
Masturbation is not a sin in Hinduism but there is energy loss. This energy loss results in saints and holy women losing their powers. Indra specifically wants this to happen. When single-minded focus is lost the saints who could oust him from his throne falls down a notch.
Similarly, when masturbation becomes an addiction and you cannot concentrate then it reflects in other aspects of life.
This is why Hinduism constantly talks about balanced approach. There needs to be a balance in all aspects of life. When one aspect of life is given too much importance, then there will be problems in the other areas of life.
The phenomenon of masturbation is not limited to human beings; even divine beings are no exception.
Masturbation and sex got the fake covering of sin in Hinduism after it came into contact with monolithic religions. The Victorian morality that was thrust on us Hindus through British education made sex and other aspects a sin.
Masturbation is a natural phenomenon and this is beautifully explained in the story of Rishyashringa. The boy was kept away from women by his father, Vibhandaka, who himself had lost self-control and lost his powers to overthrow Indra.
When Rishyashringa, as a teenager, meets a girl for the first time in his life, the feelings and physical changes that happens in him gives clear indication of masturbation.
Hinduism is never against any kinds of natural urge. We have to go through all the natural urges before we can enter the next stage of life. Putting unwanted blockages on natural urge in the name of religion only causes more harm than good.
Have a balanced approach to every aspect of life. This is what is required.
Earlier on a similar topic
Observing Hindu Vrat during Menstrual Period - Rules During Monthly Menstruation