"That'll be the day."
Ethan says this throughout the film several times, so much so that it almost becomes a catchphrase. It is emblematic of his desire to follow his own convictions and not take any flak from anyone. His insistence that "that'll be the day" is his way of telling his companions that he will buck expectations time and again.
"But what that Comanche believes, ain't got no eyes, he can't enter the spirit-land. Has to wander forever between the winds. You get it, Reverend."
After they come across a dead Comanche in the middle of the desert, Ethan brutally shoots the corpse in the face, which leads Reverend Clayton to scold him for being so cavalier and needlessly violent. Ethan rationalizes his brutality by suggesting that he wanted to make sure that the Comanche could not pass into the afterlife. This is a strange moment, in which Ethan both subscribes to the belief system of the Native Americans he so hates, while also desecrating a Comanche corpse.
"Some day this country's gonna be a fine, good place to be. Maybe it needs our bones in the ground before that time can come."
Mrs. Jorgensen suggests that, for all the sacrifices the white settlers in Texas have made, it is not for naught. Someday, she says, it will have been worth it, and they will have paved the way for the American dream to be realized in the West. It is this ethic that is at the center of all of the settlers' philosophies about life and their reasons for living in such a treacherous part of the country; they are bolstered by their belief that they are paving the way for future generations.
"Let's go home, Debbie."
After a half-hearted attempt to kill her once, Ethan suddenly switches course, and decides to bring her back to the Jorgensens' farm at the end of the film.
"What you saw wasn't Lucy... What you saw was a buck wearin' Lucy's dress. I found Lucy back in the canyon. Wrapped her in my coat, buried her with my own hands, I thought it best to keep it from ya."
After Brad comes running back to tell Marty and Ethan that he saw Lucy among the Comanche, Ethan clarifies that Lucy is actually dead, that he saw her dead body in the canyon they just passed by, but did not want to say anything about it.
"Fetch what home? The leavings a Comanche buck sold time and again to the highest bidder, with savage brats of her own?"
When Marty says he wants to go save Debbie and bring her home, Laurie says this line, revealing her own prejudice about the Comanche and Debbie's position among them. She suggests that Debbie is no longer worth saving since she integrated with the Comanche, and tries to discourage Marty from going.
"I remember, from always. At first I prayed to you to come and get me, take me home. You didn't come."
When Debbie comes to speak with Marty and Ethan, she tells them that she prayed for them to come fetch her and save her, but they never did, so she has decided to stay with the Comanche.
"Our turnin' back don't mean nothin', not in the long run. She's alive, she's safe for a while. They'll keep her and raise her as one of their own til, until she's of an age to... Injun will chase a thing till he thinks he's chased it enough. Then, he quits. Same way when he runs. Seems like he never learns there's such a thing as a critter that'll just keep comin' on. So we'll find 'em in the end, I promise you. We'll find 'em. Just as sure as a turnin' of the earth."
Marty worries that if they turn back, they will lose hope of ever finding Debbie, but Ethan assures him, with this monologue, that it will be alright. He says that they will keep searching for her, and they will find her eventually. This line shows just how determined Ethan is.
"That which we are about to receive, we thank thee, O Lord."
Mose Harper says this as a kind of joke before the Texas Rangers, led by Reverend Clayton, are attacked by Comanche warriors. Of course, an attack is hardly a "gift," but Mose has a somewhat warped sense of humor.
"Not quite, I'm eighth Cherokee, the rest is Welsh and English. Least that's what they tell me."
When Ethan first meets Ethan, he says that he looks like a "half-breed." Marty clarifies that he is actually an eighth Cherokee, defensively suggesting that the rest of his heritage is Anglo-Saxon.
