My question was why the Christians were able to reform their society, when the Hindus failed to do so. Many Hindus like to claim that Hindu society was much more liberal and inviting to change than that of Abrahamic religions, who have a reputation of being rigid and suppressing any sign of heresy or dissent. If so, how were Christian Western Europeans - the followers of an Abrahamic religion - able to create a rational, scientific civilization that far surpassed what the Hindus or any one else had created up to that point?
The modern Hindu "reform" movements such as the Brahmo Samaj and Arya Samaj all emerged in the 19th century in the context of European colonialism. The Hindus were shocked at their perceived backwardness in comparison to the Europeans, not only technologically but also (in their minds) socially and intellectually, and this prompted change among them. It was only during this time that practices such as sati and the caste system were formally denounced by Hindus. It was also during this time that many Hindu texts were re-interpreted, with the view of making them more acceptable by European standards. Ancient Indian sexual ethics and morals, for example, were discarded by Hindus as being "primitive" and "shameful", and Victorian morals were embraced. Gradually, these changes began shaping Hindu society as a whole.
The simple answer is that the Renaissance took place in Europe in an environment which encouraged patronage of the arts, science, culture, medicine, trade, commerce etc. While the Church may have persecuted individuals for what they considered to be "blasphemous" ideas, these were isolated instances and did not result in the wholesale persecution of classes or communities of people.
In India on the other hand, under Muslim rule, the majority faith was suppressed, their places of worship routinely destroyed, and the adherents persecuted. There was no state patronage for anything-the rulers saw themselves as separate and superior to the vast heathen population under them which was only supposed to be converted, taxed into extinction or killed.
In the face of overwhelming difficulties, the Brahmins became even more deeply orthodox, which often happens in such cases (e.g Muslims abroad being more Islamist/radicalized than those in the mother country). This had a negative impact on innovation and the free flow of new ideas.
How else can you explain the period around 500 BC to 600-700 AD, which is considered to be the Golden Age of Indian civilization, and which abruptly came to an end after the consolidation of Islamic regimes in North India?
Here's a great documentary series on how the Renaissance took place in Europe. Surely you will agree after watching that conditions in India (economic, social, political) were not at all conducive for such a transformation at that time.