[Jason's] family included all the demigods who fought at his side, Roman and Greek, new friends and old. He wasn't going to let anyone break his family apart. (4.12)
Calling friends "family" is a common trope in young adult novels. Count up all the characters with parental issues in this book (i.e., all of them)—is it any wonder they consider their friends closer family than their parents?
I can't die, [Jason] told himself. My friends are depending on me. (4.64)
Notice how Jason puts his friends first…even above himself. We're guessing he thinks this way because of how he's been abandoned in the past. He doesn't want anyone else to feel the same way.
[Leo] loved his friends. He'd do anything for them. But as he looked at the six of them—three couples, all focused on each other—he thought about the warning from Nemesis, the revenge goddess: You will not find a place among your brethren. You will always be the seventh wheel. (9.60)
It's hard enough being the third wheel (unless you're on a tricycle)—imagine being a seventh wheel. So even though Leo is loyal and his friends care about him, and they're really not the type to put relationships over friendships…Leo will always feel left out.
"We don't fight each other. We fight the giants. You should help us." (11.53)
We'd never expect our group of heroes to turn against each other, but their friendship surprises Nike, the goddess of victory. Why? Probably because the gods don't really have friends, so they have no problems squabbling amongst each other.
Earlier, Piper called Annabeth "the bravest person she knew" (19.36), so it's a big deal for her to be considered a friend…and to have something to offer Annabeth, when Piper is able to stay cool under pressure.
Reyna doubted she could change his feelings, but she wanted Nico to have support. All heroes deserved that. (22.29)
Reyna and Nico might not have been friends in any other situation, but they become almost inseparable after everything they go through together—and after Nico shows how brave and resourceful he can be.
"I don't run when my friends need me." (28.25)
Unless you've been under a rock for the last nine books, you should know this about Percy Jackson already…but he thinks it bears repeating. Percy will always see a quest through to the end.
"You shared your painful experiences; how can we not support you? We're friends." (32.25)
Nico and Reyna both share painful secrets from their past with each other, and it doesn't scare either of them away. In fact, because they both share a traumatic past, it brings them closer to each other.
"This will hurt, my friend," [Reyna] told Blackjack. (40.6)
Reyna cares for animals almost as much as she cares for people, and she gives Blackjack the pegasus the same medical attention she'd give a human friend.
"You have friends—or at least, people who would like to be your friend. You pushed yourself away." (47.31)
Remember the quote from (32.25)? Nico used to be super secretive and shut off from other people. This quality made it difficult for others to approach him and was a factor in his friendlessness at Camp Half-Blood.