I think the thing people don't really consider with Levi's reaction to Furlan's and Isabel's deaths was just how much those two actually meant to him personally. We have to remember that Levi, up until those two came into his life, was pretty much alone. Kenny hardly counts as any kind of company, and I think it's safe to assume that he likely left Levi on his own for long stretches of time before simply abandoning him outright. And of course we know he lost his mother at a very young age. He doesn't meet Furlan until he's more or less fully grown, and the same with Isabel. So, again, we have to remember that Levi spent his entire childhood and the early years of his adulthood completely alone. Isayama even said that Furlan and Isabel were Levi's first, actual friends. They really represented for him the first time in his life when he wasn't on his own.

So I don't think their importance to Levi on a personal level can be overstated. He came to the surface in the first place for them. To give them a better life. To help them achieve their dreams. And then he loses them not just very suddenly, but in a brutally violent way, right in front of him, with him being helpless to stop it. And that's the other thing people forget. Levi was right there and he couldn't stop them from dying, which, if you know anything about Levi of course, will tell you how much keener the pain had to have been for him. Levi's entire motivation in life is to help people. Again, that's something Isayama said. That Levi came to the surface in the first place because he wanted to help others. And yet he has to again and again face and absorb the grief of not being able to do so, despite his absolute best efforts. Remember how Levi had to watch Isabel scream out for him to save her moments before she was bitten in half by a titan. And remember how he had to watch Furlan's resigned wave goodbye as Levi tried desperately to make it to him in time. I'm talking about the manga here, now. I don't think people really consider enough just how deeply, deeply traumatizing that was for Levi, to watch not just his friends, but the only two people he could ever, really consider his family, die right in front of him, with him being helpless to save them. Especially, again, when one considers that he came to the surface in the first place to give them better lives.

So I guess my point is, the rage we see Levi display afterward is purely driven by overwhelming grief and shock, spurred on by the newness of that kind of death and it in particular happening to the two people who he was closest to in his life. Levi's been surrounded by death his entire life, and his familiarity with it and violence is obvious, even in "No Regrets". We still see, by and large, the same, stoic reaction from Levi seeing people die as we do later on in the story, with the subtle clues as to how much he actually cares present just as much. I don't really agree that Levi hated the Survey Corps and it's soldiers at first. I think Levi was afraid of growing attached to them, and so tried to keep himself at a remove and detached from their cause, and I think that was because Levi really knew himself. He knew, even then, that he had a tendency to care about people and to be deeply affected by any harm coming to them. His attempt at detachment is an attempt to shield himself from the pain of losing people he cares about. The problem for Levi is that, even when he isn't close to someone, he still cares about them. He still cares about their lives. He can't be detached, no matter how hard he tries to be. We see clear evidence of this with Levi throughout "No Regrets". Right at the very start, when he's being chased by Erwin and Mike, after Levi thinks he's managed to lose them, he says how the chase got a little hairy and how he hopes no one got hurt in the process. He doesn't even know Erwin or Mike at that point, and they're actively trying to harm him by arresting him, but he's showing concern for their well being. We see it again, too, later on, with one of the scouts on the training course deliberately cutting Levi off mid-flight and putting him in danger as a result, and Levi still not hesitating for a moment to save that same soldier's life when he was about to impale himself on a sword stuck in one of the titan dummies. And we see it when Levi expresses an obvious sense of guilt over having had to watch some of the scouts get eaten by a titan in order to figure out how to kill the thing himself. And then, at the very end, he shows concern for Hannes and the other members of his squad when he tells Furlan and Isabel to stay behind and help protect them. Hannes was nothing but shitty to Levi throughout the story, but Levi still cared about his life.

I think Levi's compassion and kindness is innate to him, and his lack of outward expression has always been the result of a life filled with trauma. Kenny describes him as the most unfriendly kid he's ever met, so even as a child, Levi lacked a real ability to outwardly express his emotions. It's never been indicative of him actually lacking emotion or empathy, though. Levi witnessed and experienced countless traumatic events from early childhood on, and that resulted in him kind of shutting down in order to protect himself, I think.

We see Levi's rage at Erwin, but I don't think it's so much a result of wounded pride or arrogance on Levi's part, or even a contempt for authority (we see Levi take orders from Furlan without any, real protest) but more a result of Erwin's inhumane treatment of Levi and his family and his direct threats to Furlan's and Isabel's lives. Even then, Levi doesn't give in to that rage until after Furlan and Isabel have been killed, and he learns of Erwin's involvement in the entire fiasco. And even still, the rage is short lived, and Levi reverts back to how we normally see him, very reserved and stoic.

Levi is certainly capable of expressions of extreme emotion. We see it in him during the RtS arc, when he takes down Zeke, and again that extreme anger is fueled by Zeke's cruelty and the obvious pleasure he displayed in killing Erwin and the other scouts. And again we see it after Levi takes Zeke down a second time in the forest, when Levi succumbs to his deep anger and grief over Zeke forcing him to kill so many of his own men and women, essentially torturing Zeke in retaliation.

I don't think Levi changes, fundamentally, from who we first meet in "No Regrets", I think he just learns to hold his emotions in more effectively as a result of experience showing him that giving in to his grief won't help anybody, and could even impair his ability to do his job. But in general, Levi has, since childhood, shown a lack of outward expression, because he grew up in an environment where showing your emotions was likely to get you hurt or killed. And again, it's never been indicative of him lacking emotion or empathy. It's just the result of trauma. If he grows more withdrawn and reserved as the series goes on, it's a result of the same. Needing to carry on in the face of unspeakable loss and despair.