When we "take rights for granted" it means that we live with good things to be expected. We life like the things we do will always be there. In this way, we do not appreciate/value it very much until they are gone.
- The "granted" part is the key in this phrase. It relates to assumptions. You think that it is "granted" that you receive these things.
"You shouldn't have taken my time for granted. Now I am leaving you."
"I took the practice for granted and did not study. Now I failed the test."
With "we cannot take any rights for granted," the speaker is saying that our rights may be taken from us one day and we must start appreciating them.