[@KatherinWinter]

[color=ed1c24]Why does he think he needs to tell her the motto?[/color]

[s]It sounds cool, and title drop.[/s] 

He told her because he was elaborating about the city itself, because he was in that city and that is topical. If we'd ever return to the city, it might be a good idea to know why the people behave that way and why he behaved in such a way toward it's citizens. 

World building. He complained in his thoughts about the city previously, trying to make it obvious that he has some kind of negative history here.

Showing off his personality, his disdain for the city and his honesty, all apart of his character. 

[color=ed1c24]But potential for what? Becoming more? Surviving? Understanding?[/color]

That's something the character can decide what he meant. It's just the characters personal and vague feelings. 

But he mentioned that the other slaves couldn't help themselves, let alone him more concrete reasons to act in such a case, goes against his character. So that's why he gave such a vague response.

(Though it's also a lie, and she closely resembles his deceased wife and that's why he picked you and had a dress of his wife as a keepsake, that fit her almost perfectly. Spoiler alert? :P)

[color=ed1c24]I understood why he needed her. But not why he offered her freedom.[/color]

Like I said he doesn't like the act of slavery. He only has her, to help get his kids back. Plus, He's desperate. 

Offering freedom seems like what any slave would -want- to hear. I think that be a good motivation for helping as well. Especially since he's being sincere about his motivations.