"She wouldn't say, but I suspect she thinks I stayed to be a spy." (1.2.135)
It's jarring to have someone you love and trust not trust you in return. For Jace, it really shakes him to have the person who doesn't trust him be his adopted mother.
"Don't call me [Jonathan]. It's not my name." (1.3.16)
Names are a big deal in this universe, where people (and objects) all seem to have multiple monikers. Keep an eye on what people are called and what they like to be called to get a glimpse of their true identity.
[Jace] seemed to be looking past Maryse, a light flickering in his eyes, as if of reflected fire. In that moment Clary couldn't help but think that he looked very like his father. (1.3.113)
This is one of the few instances Clary identifies Jace as having anything to do with Valentine. Although it's interesting that Clary refers to "his father" instead of "their father" since they allegedly share the same parentage.
"And being [a Shadowhunter]—one of the Nephilim—means everything to [Jace.]" (1.4.16)
Jace is what we mundanes know as a workaholic. It's just that Jace's job is fighting demons. Fighting demons is his life, and the Inquisitor wants to punish him by taking that away.
"I don't care who your father is either. It doesn't matter to me. You're still the same person." (1.4.94)
It's hard to decide whether this quote belongs in Identity or Family when it comes to themes. In this book, these two themes are closely intertwined, as many are defined by their parents. Can you say Sin of the Fathers?
It tore itself free of the sucking earth, crawled a few feet, and collapsed onto the ground. (2.9.59)
At first glance you might think this line is about a demon. The subject is "it" after all. But it isn't a demon. It is Simon, fresh from the ground after becoming a vampire. At first, Clary doesn't see him as even human. She sees him as an it.
"Do you even know how to use that knife, Clarissa?" (2.12.63)
Jace is a patronizing jerk, only calling Clary by her full name when he's irritated with her, like he's her dad or something.
Clary let her gaze rest on Simon, gauging the ways in which he looked both familiar and very alien. (2.12.131)
Simon physically changes after becoming a vampire, but in very subtle ways that Clary can't quite put a finger on.
It was impossible. [Jace] was a warrior. He could be nothing else. (2.13.87)
At the beginning of the book, Jace thinks that he can live as a mundane. By the end of the book, after killing a few dozen more demons, he realizes that this will never be possible.
"Maia," Simon said. "You're still human." "No, I'm not." "In the ways that count, you are. Just like me." (3.16.137)
We think Simon is reassuring himself as much as he is Maia in this situation. After becoming a vampire, Simon isn't sure who—or what—he is anymore, and he has to cling to his humanity whenever possible.