Okay so first of all at this point Emil is definitely one of my favorite characters, second only to Sigrun, and one of the things that I love about him is that he is realistically, sympathetically flawed. From what we've seen of Emil, at least in the beginning of the story, he tends to be boastful and talk himself up a lot, but I'd say that this surface arrogance is covering for a whole lot of deep, deep insecurity.
Emil's early education consisted of being taught by a lot of expensive private tutors, but it seems as if they didn't do their job. Given that he was allowed to pick his own curriculum, supposedly excelled in everything he was taught, but then crashed as soon as he entered the public school system, it isn't too hard to deduce that what in fact happened is that those tutors never corrected any of his mistakes, only gave him an endless stream of praise. Maybe his parents threatened to fire them if he did anything less than excellent in every subject, but in any case, he went from having zero actual guidance in his early life to getting little to no positive feedback when he entered public school, made even worse by the fact that he'd probably never been corrected for anything and thus had never learned how to take criticism. So instead of trying to improve himself, he instead blamed his teachers for having it in for him.
Things probably didn't improve when he joined the ranks of the cleansers; his career was slow, and if he didn't get much positive feedback in public school, he definitely didn't get any in the military. Not to mention he seems to be very poorly socialized as well; if his parents were overly indulgent and wouldn't allow his tutors to fail him in anything, they probably also didn't bother to discipline or correct him when their precious baby said something that was out of line. Recall Emil's tendency to put his foot in his mouth, to say stupid or insensitive things without thinking (the worst being when he was dismissive of the deaths of hundreds of people in the battle of Kastrup, which was a bit much for even the stoic Mikkel) yet be overly worried about superficial things like appearances.
I think that on some level, Emil knows that people don't like him. Minna has even said in the Author Notes that he hasn't had many friends in his life, and those he did have didn't stick around for long. A good part of this is his own fault, as we've seen again... and again... and again, but rereading the comic I can't help but notice how downright condescending his uncle and aunt can be when they talk to him, and find it incredibly sad that the people who should be most supportive of him seem to be the ones who are least willing to give him a chance. He might have even figured out that he has a problem with people, and that a lot of the problem is his own fault, but has chosen to fixate on the wrong thing (physical appearances, as opposed to thinking before he opens his mouth).
Which is where the insecurity comes into play. Whenever anyone speaks another language around him, Emil's default assumption seems to be that they're making fun of him behind his back, even if there's very good reason - such as Tuuri speaking Finnish with Lalli because that's the only language Lalli knows, or Mikkel speaking Icelandic with Reynir because that's the only language Reynir knows. Also note how his attitude went from boastful when he was safe in Sweden, to 'I have to prove myself!' when he was out on his first mission, and the differences in his interactions with Tuuri and Sigrun. With Tuuri, he was outright boasting about how much of a prodigy he was; with Sigrun, it seemed less like he was trying to inflate his accomplishments and more like trying to cover for his inexperience. Everything he said there was all technically true - he had faced a giant and punched it in one of its faces; he even specified that he'd faced a troll up close before once. I think that the attack on the Dalahasten was when all of this really became real for him - 'This is what being attacked by one of these monsters is actually like and I'm going right out into a No Man's Land that's infested with them and I'm working with someone who has so much more experience than me oh crap.'
Yet for all of his character flaws, when he's not being overrun by his insecurity and his own ego Emil can be a real sweetheart. He's good with kids, even his demon cousins who drove the babysitter to quit and pushed Tuuri and Lalli over the edge within minutes, doesn't hold grudges or get angry about petty things, and takes it really hard when animals die. There's also an interesting contrast in his behavior when only his life is on the line ("SIIIIIIGRUUUUUN! HEEEELP MEEE!") versus when one of his friends is in danger. In most works, a character like Emil whose fear is often played for laughs would throw his teammates to the metaphorical wolves to give himself more time to get away. Emil, though, does the exact opposite - he spends the entirety of the attack on the Dalahastan shielding Lalli with his own body, even though it's clear that he's terrified out of his mind. Not only that, but so far there have been two separate occasions where Sigrun has had to physically restrain him from rushing right into a troll nest when he was afraid for Lalli's life, even if said troll nest was on fire.
As the story's progressed we've seen less of Emil's egotistical side (though it does still rear its head from time to time) and more of his sweet side, and I think that's because he's been slowly feeling more secure. His sweet side tends to come out when he's dealing with anyone who's less likely to judge him - children, animals, and Lalli who doesn't speak the same language. I even have a pet theory that the language barrier has been an asset in his bonding with Lalli rather than a hindrance - he can't put his foot in his mouth if the other person doesn't understand a word he's saying. I think that his time with this group has been really good for him, not least because his friendship with Lalli and his apprenticeship with Sigrun especially have been the first truly positive relationships he's had in a long, long time.
