"Well, Arthur, are you a friend of Fish's?" the old man asked.
[…] The boxtroll holding Arthur's hand turned to him, squeezed his hand, and made a happy gurgling sound. (5.13-14)
After Arthur's run-in with Snatcher, he finds shelter in Willbury's home, and the boxtroll who brings him in to meet everyone, Fish, seems to take a liking to Arthur. We don't speak boxtroll (and neither does Arthur) so we don't know exactly how Fish responds to Willbury, but we get the sense that it's an enthusiastic reply.
"And these are my friends," Willbury said, looking around at the creatures. (5.21)
What is a retired lawyer doing with monster friends? We're not entirely sure, but Willbury seems to be a kind-hearted fellow who knows what's up. If he's friends with underlings, they must be okay. Knowing who's friends with whom seems to be one way to get a handle on whether someone's a good person or not, sort of like a vetting system.
"I'm warning you. GO AWAY! I do not sell friends!" Willbury was turning red. (11.29)
This is one big difference between Snatcher's camp and our crew of unlikely heroes. The villainous types don't see underlings are friend-material, while Willbury and Arthur clearly do. Snatcher and his dudes clearly don't care if they're acting in a way that totally dehumanizes the boxtrolls and cabbageheads, while Willbury sees them as close enough to human to be friendly with.
"Now we must find new homes for our other friends," Willbury said. "I want Fish, Shoe, and Egg to look after the little boxtroll, and Titus, you're in charge of the tiny cabbagehead." (11.48)
Willbury is so into his friendships with the underlings that as soon as some new underlings enter his care, he's all about assigning them buddies. It makes sense, given that the new tiny boxtroll and cabbagehead seem frightened upon arrival. We're just noticing that Willbury seems really into the idea of caring for his friends, and making sure they have both the physical and emotional resources that they need.
He looked at the children. "I don't think I have any friends." (12.6)
Aw, poor Arthur. While walking and talking with Willbury, he asks about what normal children do. Apparently playing with friends is on the list, leading Arthur to think that because he's grown up isolated from other children, he doesn't have any friends. Luckily we see Arthur getting to make friends over the course of the book, starting with Willbury and the boxtrolls, and progressing to include a whole bunch of other characters.
"Good morning, Marjorie," said Willbury. "How are you? I would like you to meet a good friend of mine, Arthur." (14.54)
See? Arthur has more friends than he thinks. Willbury introduces him as not only a friend, but a good friend. That counts for something, right? Like, yeah, Willbury feels obligated to help Arthur get underground so he can go home to Grandfather, but they also seem to share a connection. Then again, as we're seeing, Willbury considers a lot of people to be his friends.
"I'm coming too," Arthur declared. "Fish and Egg and Shoe and Titus are my friends." (16.118)
Arthur has come a long way, from being all emo and declaring that he doesn't have any friends, to saying that he's going on a potentially dangerous rescue mission to get his friends back from their kidnapping. Seems like a great tribute to the power of friendship if you ask us.
In the cell Arthur listened as Grandfather tried to jolt Herbert's memory. "Herbert, do you remember playing with me when we were boys?" (39.1)
Apparently Grandfather and Herbert used to be good friends when they were young. Based on Grandfather's stories, they used to get into all kinds of trouble while going on adventures and creating bizarre science experiments. That's what friends are for, right?
"Well, I can tell you… the size goes directly into a very special friend of mine, and as he gets bigger, he becomes more and more unstoppable!" Snatcher's good eye was nearly bulging in his excitement. (44.27)
This is one of the few times Snatcher refers to someone as his friend. In this case, the someone is an elephant-sized rat with anger management problems. We're not sure if we are more worried about Snatcher's character judgment, or if we just feel bad for him for not really having any friends.
"I loved every moment I spent living in the Underworld with you, but it's not the best place for a child to grow up. You need sunlight, and you need friends. And now you are going to have both." (54.11)
Grandfather's words to Arthur are downright sweet. They're a good reminder that while family is important (and hey, Grandfather may not be Arthur's bio-family but he did take him in as an infant and raise him), friends are an important part of growing up, too. We're glad that Arthur has gotten to make a bunch of friends over the course of the story, and that he'll get to keep living around them.