I thought about it, looking at the pictures and then at my grandfather, his face so earnest and open. What reason would he have to lie? (Prologue.38)
At this point, Jacob does believe Grandpa—which is great because Grandpa isn't lying to him. But when kids make fun of Jacob at school for believing these stories, Jacob changes his mind. It's not Grandpa who betrays Jacob at all, but the other way around.
My dad explained it to me: Grandpa had told him some of the same stories when he was a kid, and they weren't lies, exactly, but exaggerated version of the truth. (Prologue. 46)
Maybe Grandpa was upset because his own son kind of betrayed him years ago by losing trust in him.
I told [Grandpa] that a made-up story and a fairy tale were the same thing, and that fairy tales were for pants-wetting babies, and that I knew his photos and stories were fakes. I expected him to get mad or put up a fight, but instead he just said, "Okay." (Prologue.45)
Or maybe Grandpa does betray Jacob here. Why doesn't he try harder to convince him?
Even my best and only friend Ricky didn't believe me, and he'd been there. (2.14)
When no one believes him, Jacob knows how his grandfather felt all those years. And it sure doesn't feel good.
I pretended to be fine. […] I faked an entire dream journal, making my dreams sound bland and simple, the way a normal person's should be. (2.28)
Jacob tries to betray his psychiatrist by lying to him and saying he's all better, but (1) Dr. Golan is able to see right through that, like a good psychiatrist should, and (2) Dr. Golan is ultimately trying to betray Jacob by having him lead right to his grandfather's true home.
Jacob Magellan Portman
"How about when you die? Should I burn all your old manuscripts?" (2.52)
Jacob thinks it's a betrayal of his grandfather's memory if he just throws all his stuff away. But maybe it's just an age difference. What's Grandpa going to do with the stuff anyway, now that he's dead? Dad understands that, but Jacob isn't old enough to get that yet.
If Grandpa Portman wasn't honorable and good, I wasn't sure anyone could be. (4.52)
Finding out that Grandpa might be an adulterer doesn't just sting, it kind of shakes Jacob to his very core. Jacob wants to be Grandpa, but he doesn't want to be him if he's not as good of a person as he's thought.
My grandmother had bought my dad this ridiculous pink bunny costume, and he put it on and sat by the driveway waiting for Grandpa Portman to come home from five o'clock until nightfall, but he never did. (4.29)
Lots of Dad's resentment for Grandpa comes from this time when Grandpa didn't come home for Halloween. Their relationship never quite recovered from this betrayal of trust between father and son.
I sat down with the box in my lap and untied the string. (8.153)
Jacob doesn't seem to have any guilt or hesitation about betraying Emma's trust and looking into her private things. Why is that? Does he feel entitled to any information about his grandfather, or does he not quite see her as a real person with real feelings?
Jacob Magellan Portman
"Instead you tried to seduce me with food and fun and girls while keeping all the bad things a secret?" (9.48)
Jacob feels betrayed by Miss Peregrine because she's a little selective with the information she chooses to tell him. Does he have a point? Is she manipulating him?