Arthur and Garth's relationship is so complex that saying they have a parent/child relationship is not accurate in the slightest. And thats a bit odd considering Garth fits the "adopted orphan trope" that half of the fab five, but while Dick and Roy have issues with Bruce and Ollie, they never reach this level of detachment because of them.
First of all, both Garth and Arthur share a similar past. They were both abandoned and left on a reef, which might be one of the reasons why Arthur choses to take him in.
And it's all really sweet! Garth is really just kid who takes an immediate liking to Arthur, and while Arthur tells him to behave, he is pretty content too.
Things continue like that for a while, Garth plays matchup with Mera and Arthur and in no time they are about to have a kid. This, among Arthur's status as king makes Garth question his role in the family and feels a sense of estrangement towards both Arthur and Mera.
Arthur Jr is born though, and Garth takes care of him as an older brother for a bit. But then Garth and Arthur Jr's life are placed on a balance.
And Arthur really doesn't think twice.
This is something you might be familiar with, as it becomes a very important part in Arthur and Garth's relationship, and Garth's search about his origin and family.
Most of their arguments revolve around this event, a lack of trust and most importantly, Arthur’s issues.
and this is something I don’t see many people talk about (mostly cause the Garth fandom is really really small) but what this lead to was meant was that Garth had to grow up too fast. He was on his own before Arthur found him and then got rejected by him.
But at his core Garth, still cared about Arthur (and so did Arthur, he was just to blinded by hate and grief to truly show it), and since Arthur was struggling, Garth almost plays the role of a character at times, which is the exact opposite go one what would expect in this type of relationship.
Arthur though, wasn’t necessarily forced to act as a father figure to Garth, but it is still sad because that’s something Garth needed and craved.
And perhaps Arthur should be held accountable. but you can still feel empathy for him. He didn’t just neglect his relationship with Garth, he did so too with everyone he knew. That will never justify hurting someone you're entirely responsible for, but it is at its core a man ruled by grief.
Again, while they didn't always fit the traditional family dynamic, their issues mostly stem from this event. And thats something that with time, they are finally able to leave behind.
Now, does that mean their relationship is fixed? Not really. Even when all is forgiven, they both progressed by themselves so much so that they don't express a familial bond. There is just something so strong about the wording and the language they use to refer to each other, especially on Garth's part.
They usually call each other a friend, and it's Mera's husband and his son and his people, and that's entirely due to their actions. Garth has a history of feeling like an outsider and this is something that I believed his relationship with the Aquafamily only strengthened. Arthur refers to him as his son I think two times in the entirety of the comics (though correct me on that if Im wrong).
Sure, language isn't always a way to show the emotional bond between two people, but I do believe that Garth doesn’t think of Arthur as anything other than a friend, at least at that moment of their lives. And that's not a bad thing in itself, because not everything has to fit the nuclear family dynamic! But it is a shame because Garth did see Arthur as a father figure and he still had to figure out so much on his own, including dealing with grief over Tula's death, because Arthur was neither in conditions to help, nor had he shown him that he was willing to.