"I must have her, even though I injure her butterfly wings."
In spite of Sharpless telling Pinkerton that he ought not marry an impressionable girl if he does not plan to be faithful to her, Pinkerton uses this line to communicate that he cannot resist himself. Even though he knows he might hurt Butterfly, he wants to possess her in marriage.
"I am following my destiny."
Butterfly describes how she converted to Christianity in order to more completely adhere to her new husband's beliefs, culture, and religion. She describes it as her destiny to completely merge with him, including his religious beliefs.
"I have caught you. You are mine."
After Butterfly gets disowned by her family, he tries to comfort her, by telling her that he will take care of her. However, he cannot help but use a metaphor of possession to communicate this. Furthermore, he plans to abandon her in due time.
"I do not think I am; I am."
After three years have passed, Butterfly believes that she is still married to Pinkerton. She stubbornly refuses to accept that she has been abandoned and does not believe that she is free to remarry, resisting Goro's well-intentioned efforts to find her another husband. In this moment, she insists that she knows that she is married to Pinkerton, and that it is not a matter of belief.
"Let him die with honor who cannot live with honor."
One of Butterfly's cherished possessions is a knife used by her father to commit ritual suicide. At the end of the opera, when she realizes that she has no choice but to give up her child to Pinkerton and Kate, Butterfly rediscovers Japanese customs and chooses to kill herself, so as to die with honor after being dishonored in her marriage to Pinkerton.
"In this country, houses and contracts are flexible"
Pinkerton says this early on in the opera, referring to the fact that he now is in possession of a house, but could easily give it up. This line foreshadows the way that Pinkerton does not take his Japanese commitments very seriously, including his commitment to Butterfly.
"Something in her voice touched me. That's the way love sounds when it is sincere. It would be a terrible sin to break those frail wings."
In the first Act, Sharpless tries to warn Pinkerton that Butterfly is genuinely in love with him, and suggests that he ought not to be too careless with her feelings, since they are genuine.
"I am the happiest girl in the Japan—no, in the world."
As Butterfly arrives at the house she is set to share with Pinkerton, she sings about how she is very happy. She suggests she is the happiest girl in Japan, before amending her statement to say that she's the happiest girl in the world. This shows just how excited she is to marry Pinkerton.
"One fine day we'll see a trail of smoke rising from the edge of the sea."
In Act 2, when Suzuki suggests to Butterfly that she thinks Pinkerton may not return, Butterfly insists that he will, and sings an aria (one of the most famous in this opera, and indeed in all of opera) about her faith in the fact that "one fine day" Pinkerton will return to her and be her husband.
"Take a good long look and remember your mother's face."
Right before she commits suicide, Butterfly calmly sits down her young son and instructs him to study her face to always remember it after she is dead. It is a heartbreaking moment of farewell.
