Imagine the scene. In those days, India had just broken free from the colonial yoke, and was anxious to establish itself as an independent entity in the comity of nations. The leaders of India had to let the world, and not so much the people of India, know that the new Indian nation had arrived. Contrary to popular belief, therefore, the intended audience of the Preamble of the Constitution of India were not so much the people of India, but the leaders of the numerous nations of the world at that time. This is, of course, true of all constitutions.
When they wrote 'We, the people of India...give to ourselves this Constitution', therefore, they only meant that it was not the people of Britain, or any external entity, giving India a Constitution, but Indians themselves. Recall that that was the top concern at that moment: who decides for India? Indians or foreigners?
Now, this may appear like stating the obvious, and therefore unimportant, but it is not. The sentence 'We, the people of India...give ourselves this Constitution' has two important meanings with a world of difference between them. They are: (a) the people of India, represented equally and fairly in some sense by the Constituent Assembly, give themselves this Constitution, and (b) the people of India as different from the people of Britain, give themselves this Constitution.
We think, and we are taught, that the Constitution of India is based on the former understanding, but that is wrong. It is based on the latter understanding in which equal or fair representation of Indians of all descriptions is neither necessary nor implicit. Even if the framers of the Constitution are a handful of people from some corner of India, culturally alien to most of India, they can still get away with describing themselves as 'We, the people of India'. One only has to ensure that they are not foreigners, say Britishers.
And that is what we have today. The Constitution of India is a document authored, in the ultimate analysis, by a handful of people from North India who claimed to represent all of India, while in fact they hardly represented North India itself. It draws a line between an Indian and a non-Indian, considering the peoples of India as one in all respects by virtue of their newly imposed Indian identity. As far as drawing lines within India is concerned, the Constitution considers it to be a necessary evil at best.
But that does not render the Constitution culturally unbiased as one might expect, and as the world has been led to believe. There is such a degree of northern bias in the Constitution, including the open partiality towards Hindi and its speakers, and the consequent atrophy to which languages like Kannada have been pushed, that Kannadigas and other South Indians might as well read the Preamble to the Constitution of India as 'They, the people of North India....give to us all this Constitution'.