In chapters 1-6, which quotes fit this theme: Inequality in treatment between whites and blacks is very apparent in the narrative.
There are lots of quotes that help illustrate the very apparent inequality in the treatment of white and black people in Narrative of the Life of Frederick Douglass. Here are a couple quotes to get you started!
The white children could tell their ages. I could not tell why I ought to be deprived of the same privilege. ...
By far the larger part of the slaves know as little of their ages as horses know of theirs, and it is the wish of most masters within my knowledge to keep their slaves thus ignorant. I do not remember to have ever met a slave who could tell of his birthday.(Chapter 1)
As a slave, Frederick Douglass is deprived of even basic knowledge he clearly has a right to: knowledge about himself.
I looked for home elsewhere, and was confident of finding none which I should relish less than the one which I was leaving. If, however, I found in my new home hardship, hunger, whipping, and nakedness, I had the consolation that I should not have escaped any one of them by staying. (Chapter 5)
This one speaks pretty clearly for itself of the terrible privations and punishments slaves faced as a part of daily life at "home" on a master's plantation or elsewhere.
He was immediately chained and handcuffed; and thus, without a moment's warning, he was snatched away, and forever sundered, from his family and friends, by a hand more unrelenting than death. (Chapter 3)
Slaves could also be sold and removed from their families at a moment's notice, without their consent.
"Learning would spoil the best n***** in the world. Now," said he, "if you teach that n***** (speaking of myself) how to read, there would be no keeping him. It would forever unfit him to be a slave. He would at once become unmanageable, and of no value to his master. As to himself, it could do him no good, but a great deal of harm. It would make him discontented and unhappy." ... I now understood what had been to me a most perplexing difficulty--to wit, the white man's power to enslave the black man. (Chapter 6)
Slaves are not given the right to an education—in particular, the right to learn to read. Here Frederick Douglass tells us that many, including Mr. Auld, believe it is because it would give a slave too great a power over his master; he would be a slave no longer.