If it meant that I'd finally be able to put my grandfather's mystery to rest and get on with my unextraordinary life, anything I had to endure would be worth it. (1.129)
Jacob realizes that his fate is at stake here. He can be cowardly and stay home, or he can be brave and pursue his grandfather's past and his own future.
"They're coming for me, understand? […] What am I supposed to fight them with, the goddamned butter knife?" (1.24)
Grandpa is either senile in thinking monsters are after him, or brave for wanting to stand up and fight them. At this point, it's difficult to tell which.
I picked up the flashlight and stepped toward the trees. (1.79)
Even though he isn't armed with anything more than a flashlight, Jacob heads into the forest to find his grandfather. That takes courage. Who knows what lurks in the woods of Florida? Alligators, rabid theme park mascots—anything could be out there.
Jacob Magellan Portman
"I got a .22 in my trunk. You just wait." And he walked off to retrieve it. (1.77)
It's a good thing Jacob has brave friends, too. Well, owning a gun is either "brave" or just kind of a Florida thing. We're not sure which.
I thought of all the horrors Grandpa Portman had faced in his life, and felt my resolve harden. If there was anyone to find inside, I would find them. (3.120)
Jacob's grandfather was a brave man, so Jacob uses his memory of Grandpa's courage to motivate himself to push through difficult situations.
"A young man, not much older than this boy here. […] Walked into town the morning after with not a scratch upon him. […] He only spoke once, to ask my father when the next boat was leaving for the mainland. Said he wanted to take up arms directly and kill the damned monsters who murdered his people." (4.117)
Here's an illustration of just how brave Grandpa was: Even though he's basically alone in the world, he's willing to not only keep fighting monsters, but to head off to another land to do it.
I got excited—and then just as quickly went cold, because something dreadful occurred to me. I have to go down there. (5.33)
Jacob's bravery has its limits. Going inside Miss Peregrine's dilapidated house is scary enough, but heading into the dark, creepy basement takes a new level of courage Jacob has to tap into. We feel you, dude.
Their sudden movement knocked something loose in me and I found my voice again and shouted for them to wait, but they were already pounding the floorboards toward the door. (5.61)
If we were in his shoes, we might head in the other direction, but when Jacob spots a small group of creepy kids, one of whom can generate fire with her hands, he actually follows them.
"He said he wouldn't be able to live with himself if he sat out the war while his people were being hunted and killed." (8.172)
Here's the reason Grandpa spent his life fighting monsters: It's a combination of bravery and honor at the core of his personality.
It was like hanging from the back of a speeding train. Bronwyn was terrifying: She bellowed like a barbarian, the veins in her neck bulging, with Millard's blood smeared all over her arms and back. (10.494)
All the peculiar children get a moment to show their own courage, and here's Bronwyn's. She charges right at a man who has a gun, and she has a wounded friend on her back. That's practically superhuman.