The Constitution of India doesn't tell you what India is. Because in practice, India is medieval, feudal, deeply divided across caste and communal lines, and ruled not by laws but by patriarchal power structures. Everyday India has very little to do with the India described by the Constitution of India.
What the Constitution of India really is, is a statement of intent. It describes the India that we want to be. It lays down the rules for an India that existed in the dreams of this country's founding mothers and fathers.
It says all Indians are equal in the eyes of the law because they knew that's not what India was. It says that religion should play no role in the decisions of the government because they knew it often did. It says people have the right to express themselves because they knew people often can't.
The Constitution of India is a dream. It is what this country can be, must be, and will be. It is a document through which our greatest heroes assert their wills decades after their mortal bodies have withered away. When you see young people on the road reading "we the people" out loud, what you are really seeing is a slice of that imaginary India, through the veil that is the mundane reality of corrupt, communal, and casteist India.
It's not visible to most people. So if you can see it, consider yourself fortunate. The martyrs are smiling upon you.