So what we have here is Dick showing up at Logan's door at the end of S3E1, and Logan telling him he can stay there, followed by Dick completely breaking down and Logan literally being a shoulder to cry on (side note: This was the first episode of VM I ever saw, and to say that I was confused by this would be an understatement. This whole thing makes literally no sense without S2 context).
But it's what isn't being said or done in this scene that makes it so important. So let's put it in context shall we?
Season 2 ended with the reveal that Cassidy, Dick's little brother, was a mass-murderer and also a rapist. He then threw himself off the roof of the Neptune Grand, the same hotel where Logan lives. And Logan, who is Dick's friend, was there on the roof when it happened. Now, a quick look at the S3E1 interaction between Logan and Dick, and Dick's actions, prior to this scene:
Logan: Guess who I saw on campus today?
Veronica: Some girl going wild?
L: No, my BFF, Dick.
V: I thought he was crashing with his dad in the Caymans.
L: Naw, he's back.
V: You guys talk?
L: Yeah, but it was brief. Shouted his name, flipped me off...the bonds of friendship.
L: Hey, uh... people are saying Dick's a mess, on account of his, uh, brother Greg Louganising off of my roof.
V: It wasn't your fault Cassidy jumped.
L: Nothing's ever my fault.
Dick crashes a rally held by a campus feminist group,about the rapes that have been going on, and he pretends to be having sex with a blow-up doll.
Dick goes looking for Mac's roommate, and finds Mac instead. He's drunk.
Dick: My brother never cared about, you know? You were just his beard.
Veronica (to Logan): Look, it's your BFF, the town drunk.
Dick is trying to chat up a random girl in the cafeteria.
D: Hi, my name's Dick. What's yours?
Dee Dee: Dee Dee
D: How long have we known each other, Dee Dee?
D: So, where's this going Dee Dee? I mean is this thing we feel real or are just in this for the torso butter?
Logan and Veronica are watching the whole thing go down, getting increasingly concerned.
D: Truth is, I've been kicked out of on-campus housing, and I know timing's a little sooner than we hoped for but what do you say we move in together? Make our own love nest.
DD: You should really walk away.
D: You'd like that wouldn't you? I'll admit it. The kid looks good walking away. It's all me too. Ass like Marky Mark and the entire funky bunch.
A big guy grabs Dick from behind and throws him to the ground. Logan asks Veronica for her bag. She swings it over to him, and Logan grabs it. In the meantime, Dick tries to stand up, and the guy punches him back down. It happens again. The guy lifts Dick to a standing position, and Dick just looks at him, making no move to fight back. Before the guy gets another punch in, Logan hits him from behind with Veronica's taser.
D: What? Do you want a hug or something?
Dick storms out, and Logan tells Veronica that he's going to try and talk to him.
So basically, the entire episode, Dick is being an ass to everyone, including Logan, who seems to want to help. In the end, Dick does end up letting Logan help, because, as he says, he has nowhere else to go. And this is where I get into Logan.
Logan does not have to let him in. He does not have to try and help. But he does. And, yeah, part of that is due to his feeling guilty that he didn't stop Cassidy from jumping. But not all of it. Because, at the end of the day, Cassidy hurt people that Logan cares about. And Logan isn't quick to forgive that. So I would argue that he really doesn't feel all that bad that Cassidy is dead. His actions are primarily driven by an understanding of Dick's actions. Logan has been there, in more ways than one, and that's what makes him want to help.
Dick is lashing out and making a fool of himself and being awful to anyone he perceives as having any connection to Cassidy (Logan, Mac). His behavior is reprehensible. And this is Dick, so his behavior has always left something to be desired, but in this situation, Logan (and also Veronica, because she absolutely knows what's up) see's it for what it is. A coping mechanism. Dick is acting the way he is, because he doesn't know how to deal with Cassidy's death, or the things Cassidy did, or the things that were done to Cassidy, or his feelings of guilt about Cassidy's childhood. And Logan? Logan has been there. Over and over, in S1 and S2 we see Logan responding to things in the exact same way. The beginning of S1 features a Logan who is acting out, and doing stupid things, and being horrible to Veronica. And a lot of that behavior is due to his inability to cope with Lilly's death, and his feelings of guilt about her death. Logan reacts to highly emotional situations by lashing out, or being irrational. And when Dick does the exact same thing, he recognizes it. He see's what's happening, and he wants to help.
Not to mention the parallel's between Dick's family and Logan's. Dick's father was emotionally abusive to Cassidy (and to Dick, in a different way). Logan's father was physically abusive towards Logan (and emotionally abusive towards Trina, to a certain extent). Their mother's were absent. Either literally in Dick's case, or emotionally in Logan's. Both of them lost a family member to suicide. Cassidy jumped off a roof, Lynn jumped off a bridge. And they both have murderers in their family, and perceived blood on their hands. Logan is always going to feel partially responsible for Lilly's death, and Dick is always going to feel partially responsible for everyone that Cassidy killed.
So Logan gets it. And because he gets it, he can give Dick what he desperately needs. Someone who isn't going to yell, or judge, or tell him to get his act together. Someone who is going to say "You can stay here," no questions asked. Someone who knows that "I messed up bad" isn't totally in reference to recent behavior. Someone to say "It's gonna be okay," because he knows that it will, eventually, even if it doesn't feel like it right now. Someone who will hold him while he cries.
Dick needs that. And Logan needs that. They need each other in S3, because they both need someone that knows. Someone who isn't going to judge them for doing what they can to make it through another day. And it pays off. Dick gets a little better, and it seems like by the end of the season, he's on the right track (and I will be forever bitter that the series ended, and we never got see whatever was in store for him). And when Logan needs a friend, Dick is there, in his own way, and he helps.
This has been a post. A post of word and feelings vomit