Hinduism as a term is not very old, not more than about 1000 years old.
The term first appeared during the time Muslims invaded India (about 1200-1000 CE) and called the people living on the other side of the “Sindhu River” Hindhus; like so many foreign invaders before them, they simply could not pronounce the local language correctly.
Later, when the British with its money- and power-hungry East India Company came to India in the 1600s, to loot and pillage, like all great empires and imperialists do, simply to turn a profit, they gradually gave that term nationalistic shape and recognition.
So, Hinduism is not very old at all…. the Vedas are old, Yoga is old, Tantra is old, Shaivism is old, etc., etc., but not Hinduism.
So, Hinduism is a foreign construct. Before Hinduism, India was, and still is, a conglomerate of religions and spiritual paths—a colorful universe of belief systems and mystical practices.
The two greatest and most influential, the Vedic and the Tantric/Yogic are what forms the backbone, flesh, heart and soul of India’s culture and heritage, not Hinduism.
Indeed, Hinduism was a term invented by invaders and later adopted by the Indians themselves, under pressure to conform to nationalistic and cultural currents from the outside.
Just ask Patanjali, who gave us the Yoga Sutras, just ask Krishna who gave us the Bhagavad Gita, just ask Kapila who gave us Samkhya philosophy, just ask Yudishtira who first taught pranayama on a large scale, just ask Asthavakra who wrote a Vedantic masterpiece, all great yogis, but no, none of them called themselves Hindus. Not a single one.
Hinduism is largely a modern construct. Go to India and ask an old sadhu yourself what he calls himself. You’ll likely hear him say he belongs to such and such lineage and sect, a follower of Shiva, or Rama… He most likely won’t say anything about Hinduism.
Or ask me. I will tell you quite firmly that I am not a Hindu. I am a Tantric yogi. Or just ask your yoga teacher down the road…. or yourself.
For a more in depth look at the history of Indian spirituality, and Tantra and Yoga in particular, please read: http://www.elephantjournal.com/2010/04/how-old-is-yoga-reply-to-waylon-lewis/