It is known that Hinduism is one of the oldest religions.
But why is it so difficult to date the beginning of Hinduism. We have a lot of scriptures and texts which give us a lot of information but why are scholars still debating as to when Hinduism actually began?
In ancient period, Hinduism was known as "Sanatana Dharma".
Sanatana Dharma is by its very essence a term that is devoid of sectarian leanings or ideological divisions. This is evident by the very term itself. The two words, "Sanatana Dharma", come from the ancient Sanskrit language. 'Sanatana' is a Sanskrit word that denotes that which which is Anadi (beginningless), Anantha (endless) and does not cease to be, that which is eternal and everlasting. With its rich connotations, Dharma is not translatable to any other language. Dharma is from dhri, meaning to hold together, to sustain. Its approximate meaning is "Natural Law," or those principles of reality which are inherent in the very nature and design of the universe. Thus the term Sanatana Dharma can be roughly translated to mean 'the natural, ancient and eternal way.' [Source: veda.wikidot.com/sanatana-dharma]
So, the simple answer is Hinduism was actually not a religion but a common practice which was being followed by our ancestors. So there is no question of a starting point for Hinduism or Sanatana Dharma.
Other references:
To put honestly, Indians are very bad at recording or documenting stuffs.
It's fairly accepted that Hinduism can be attributed to the origins of Veda, the oldest one being Rg Veda, we have to look for the origins of Rg Veda.
Rig Veda was for a long time transmitted orally because scriptures in Hinduism have a strict oral tradition and the language Sanskrit and the scriptures were composed taking this into account.
Now, even the time when Rg Veda was first penned down isn't documented making it very difficult to get the time-line of Rg Veda being composed.
Max Muller attributes Rig Veda to be composed at around 1500-2000 B.C. but there have been allegations of this time-line being biased as one can read AncientHistory, ThenAgain, HKNet, Controversies in History.
India does not have a documented history. The history has been reconstructed from monuments and cultural documents. The task has been made more difficult because all the kings started their own calendars. So, to put a firm date on anything is well nigh impossible. Also, consider the fact that the ancient texts were not written but verbally transmitted from teacher to pupil. And hence, it is not possible to attribute a date to the beginning of Hinduism.
Even though there is already an accepted answer to this question (which I don't agree with), I would like to point out the fact, that scientifically speaking, already the term "Hinduism" is much more complex than "Christianity" or "Islam", which of course also renders the dating business much more difficult.
While some people identify the two, scientists of religion generally differentiate between the Vedic religion of sacrifice and "classical Hinduism". So depending on what you are talking about, also the answer varies. If we identify the two, then @Vineet Menon is perfectly right to let the history of Hinduism start with the oldest parts of the Rigveda (not earlier than 1500 BC).
If we don't, then we can let "classical Hinduism" start for example with the rise of the 6 orthodox systems of philosophy, in all probability essentially as a reaction to the philosophical and numerical winning of ground of Buddhism. We can date this somewhere between 200 BCE and 200 CE (here we can expand the discussion limitlessly). Even in this case, the Vedic Religion, though not identical with Hinduism, remains its ancestor.
Conclusion: it is very much a question of how we define "Hinduism". Since we don't have a single (historical) founder of the religion and no clear cut starting date, this is open to debate (and personal liking). To give an example: Some (many?) Hindus regard Buddha as an avatar of Vishnu and therefore Buddhists as Hindus. Most (all?) Buddhists would disagree. Same holds true, to a lesser extent, with Jesus.
