Antonio's parents are an exercise in the "opposites attract" theory. They stand opposed on so many things. His father even says to Antonio, "we lived two different lives, your mother and I" (22.141-142).
His mother is a Luna. Her people are farmers who stay in one place and work the land. Devoutly Catholic, she wants Antonio to embrace his Luna blood and become a priest who will lead the Lunas one day.
His Father is a Márez. A man connected to the sea and the wind and all things that wander. He was a vaquero in his youth, and he longs to roam the lands of the llano. He's not particularly religious, and he wants his son to grow into a Márez man, a man who roams and works.
The differences between these two characters and the family lines they belong to serve as the core struggle for Antonio. There are multiple opposing forces pulling at him, but they almost always come down to whether he will choose to be Luna or a Márez (or maybe a bit of both?).