How can I analyze this quotation from Antigone? Haemon: Yours am I, father; and you guide my steps With your good counsels, which for my part I Will follow closely; for there is no marriage shall occupy a larger place with me than your direction, in the path of honour. Creon: So is it right, my son, to be disposed— In everything to back your father’s quarrel. It is for this men pray to breed and rear In their homes dutiful offspring— to requite The foe with evil, and their father’s friend Honour, as did their father. Whoso gets Children unserviceable—what else could he Be said to breed, but troubles to himself, And store of laughter for his enemies? Nay, never fling away your wits, my son, Through liking for a woman . . . (Sophocles 25)

Haemon is the son of King Creon and Antigone's fiancé. By this stage in the play Creon has already made the fateful decision not to bury Polyneices's body and instead to leave it to rot on the battlefield. He's also imprisoned Antigone for attempting to bury her brother. It might be thought that as Haemon is now engaged to Antigone he would be sympathetic to her plight. But, initially at least, Haemon shows great loyalty to his father and king:

"Father, I am yours, and you keep me upright with precepts good for me—precepts I shall follow. No marriage will be deemed by me more important than your good guidance."

Haemon is putting his father before his fiancé. He makes it clear that Creon's fatherly advice is much more important to him than his forthcoming marriage to Antigone.
Creon is clearly pleased with this show of filial piety from Haemon:

"Yes, my son, this is the spirit you should maintain in your heart—to stand behind your father's will in all things. It is for this that men pray: to sire and raise in their homes children who are obedient, that they may requite their father's enemy with evil and honor his friend, just as their father does. [645] But the man who begets unhelpful children—what would you say that he has sown except miseries for himself and abundant exultation for his enemies? Never, then, my son, banish your reason for pleasure on account of a woman . . . "

Not surprisingly, Creon agrees with Haemon's decision to follow his guidance in all things. He's not just a king, but a traditional father of the ancient Greek world. As such, he expects absolutely loyalty from his children as much as he would from any of his subjects. He also reveals the subordinate status of women in ancient Greek society. Women are weak and emotional and as such should not be allowed to prevail over man's reason. The implication here is that Antigone has acted impulsively in defying Creon, whereas Haemon is being rational in standing by his father.
The above quotations from Antigone help to set the scene for what is to follow. Haemon's reaction to this father's decision not to allow Polyneices to be buried is almost the exact opposite of that of his intended. Antigone has put her loyalty to the gods and to her brother above that of her king and future father-in-law. Haemon does the reverse.
But later on in this exchange, Haemon reveals a profound sense of unease at Creon's imprisonment of Antigone for insubordination, and eventually father and son engage in a heated argument which ends with Haemon storming off, vowing never to see his father again. So by the end of the scene we can see that Haemon is developing the kind of understanding of Creon's stubborn nature, and the injustice to which it leads, that cost Antigone her freedom. For Haemon, the scene begins in childhood but ends in maturity, from an expression of conventional Greek filial piety to the getting of moral wisdom.