To what extent The Constitution be said to grant freedom and cause oppression?
This is an interesting question. I am not certain that the Constitution, as it is constructed now, is designed to create or cause oppression. One could argue that the Constitution's conception of freedom and action arising from government and coming from "the top down" denies the essence of power originating from "the bottom up," but there is little within the Constitution as it is constructed now to outwardly rule against such a concept. At the same time, the original Constitution did grant freedom but only to a select few. The original version of the Constitution which came out of the Constitutional Convention did little to address the suffering and oppression of African- Americans and Women, and also featured little in way of assistance to those who were economically challenged. This became a critical element that might not have caused oppression, but did not allow for a full expression of voices in America.
I would not agree that the original Constitution granted freedom to "only a few." The original Constitution as it was written granted freedom to everyone except to slaves (which is a huge omission).
The guarantees of freedom found in the Constitution and the Bill of Rights was not limited to any particular group. Both men and women were granted the right to freedom of speech, religion, etc.
It is true that women were subjugated during this time, but this is not from anything that is in the Constitution. There is nothing in that document that differentiates between women and men.
So the document grants freedom by explicitly specifying a number of freedoms that are protected from government interference.
In my opinion, the oppression that occurred in early America was not caused by the Constitution -- it was caused by the societal values of the time.