Kanda has been living at the Order and fighting in the war for as long as he's been alive. All he knows is battle, and it shows. He not only has the lowest IQ of our main four, but he also has a measly 2/5 in the education department. Not that he's a complete idiot, he can have common sense when it comes to the things he's actually good at, but he's no learner. He has difficulty understanding other people, and his skills fall towards the physical. Even then, the only things he's stated to do are meditate (less of a stimulating activity and more of a calming one), garden (to which we are unaware of how good he actually is at it), make soba (see last parenthesis note) and do his job. Which is fighting. This hardly seems to concern him. He's also not religious, caring as little about God and holiness and sin and the afterlife as he does the war itself. His dislikes are often put as "too many to list" but some have been specified, such as crowds or people who can't keep their promises.
To most people, Kanda is seen as a rude, careless, temperamental, intolerable, childish asshole. He's got a short fuse, poor social skills, a general apathy towards people, grating arrogance, stubborn behavior, violent tendencies, and a sour disposition that makes the majority of people prefer to steer clear of him. And they're not entirely off the mark-- it's just that most people don't see anything but a handful of his traits (and he much prefers it that way). There's also to Kanda a sense of loyalty and dedication, of hurt and vulnerability, of underdevelopment, of drive, and even of love.
Generally, Kanda's default behavior is aloof and apathetic with a nice peppering of grumpy. He's careless towards people and isn't concerned with reigning in his often rude and tactless behavior, not bothered with upsetting other people that he doesn't know or care about. He's cold and distant, he's unsociable with a pessimistic view on life and a leaning towards very sour behavior. While not naturally angry, he is volatile and has an exaggerated temper that's quick and easy to set off and often ends in childish screaming and retorting and even violence. He's stuck in his ways and while aware that other people don't care for his behavior, he doesn't care enough to bother changing it. They can like it or leave it.
This part of Kanda is a sort of half-mask for him. It's genuine behavior, not something he's faking for the sake of saving face. But it's usually the only part of him he lets out in the open. It's a defense, a barrier so that he can keep the world at a distance and they can't come in and hurt him any more than he already has been.
Despite his tactless behavior, he also actually can be polite and cooperative when he needs to be. Much as he'd rather just not deal with people, he can say thanks and keep his attitude in check. Most often this seems to be on missions, and probably makes it easier to deal with people in as short of a manner as possible anyway, so it's still self serving. Authority is something else he can actually treat with respect when they deserve it or because he has to.
He's also proud. Very proud. This can only make his stubbornness worse, because like hell if it means he'll allow it to be wounded. His arrogance is most seem in the battlefield, but it swells whenever things go his way. And if they don't, he'll fight back just to keep himself from being made a fool of. He'll take his respect and his skill, and he'll rub it in your face, too. It's perhaps his reality that makes him strive so much to be better than others, and to keep them below him simply based on the fact that he's stronger, faster, and chosen for what many of them were not. He's meant for fighting, through and through, and he can't bring himself to be inferior at the one thing that actually makes him worth something, that isn't as expendable.
Kanda has a stubborn streak to a fault, and coupled with that an intense sense of drive and loyalty. He refuses to stand down when in battle to the point of recklessness, suffering fatal injury after fatal injury and wearing down the time he has left to live with his mostly nonstrategic fighting, using his regeneration as a crutch. He's dedicated to doing his job and doing it well, even when he doesn't actually care about the war he's fighting, or even the organization he's fighting for. Nine years where he could have defected and abandoned his Innocence and his job at any time, and he hasn't. He's a solider, one of few selected to save the world, and damned if he isn't going to do it. Damned if he won't do it while still working for the Order. He throws himself into battle against a level 4 Akuma even without his Innocence to save their Supervisor from certain death. Dangerous, possibly deadly, yes, but he'll defend and stick to the higher authority, even if he doesn't like it. It helps he's not exactly much of an individual thinker, falling into a subordinate roll despite his strength and strong will. He also has a stubborn denial of things that don't fit into his worldview. Despite recognizing Alma for who he was, actually alive when he figured him dead, he insists he has no idea who they are and continually asks to be told such. The more they explain who he really is, though, the more upset and angry Kanda gets, frustrated with the difficulty to continue to pretend that things are exactly as they are. He refuses to acknowledge fallacies in his own viewpoints and lifestyle if he can help it. He doesn't deal well with change.
He has a strong drive to do his job. He doesn't like it, but he's aware that he's basically a human weapon, a tool for the Order to use even when his service should have been over. But an even stronger drive to complete his personal goal. "That Person" (Alma), a woman from his past life, whom he can seemingly remember nothing about. Finding her so that he can keep his promise is the only reason he has continued living through his miserable existence, and chose to murder his best friend over allowing them to die as they were meant to. He's determined to take her to the blooming lotus field before he even dares think about dying. He has intense determination in fulfilling this single life goal that he's set for himself. He even keeps a lotus in an hourglass in his room as a memento of his goal. He said he'd take her before the last petal fell, so what better way to track that than an actual lotus flower to remind him? Along with that, he's very strong about keeping promises. Allen manages to infuriate him by nearly failing to keep one of his own on his first mission. He's fighting tooth and nail to live to keep one of his own. No matter what the probability is, if it's been promised, it should be fulfilled.
He is also a hypocrite. He's quick to tell people he doesn't care about them, doesn't care if they die, doesn't care about anything but his job. And the very next mission, he's taking the deadly bullets or defending their ass before they're ash and clothing. Does he means he liked them? Not necessarily, but it does mean he understands comradeship. He may act like finders are inferior or other Exorcists lives don't matter, but he knows that they're on the same side and so he'll defend them regardless of what he thinks. He has an arrogant streak and a dominance over other characters, and yet he's resigned himself to be used like a weapon for the Order, following his missions through without failure despite the way he's been treated by Central.
His whole personality and mindset really suffers from underdevelopment, really. Having only nine years of world experience and all the lack of emotional development from being in a war setting that whole time does that to you. He has an inability to handle most social interaction properly, is severely lacking in the skill of tact, and generally doesn't give a damn about most things. He doesn't handle his own emotions well and keep things unhealthily bottled up, because he can't bring himself to let anything out into the open. He's rather self-destructive in his actions, careless on the battlefield and allowing himself to hide his weakness rather than confront it. He even shuts down his thinking completely in his latest fight with Alma, just acting on total (insane) instinct because he doesn't want to face all the emotional pain. He's bitter about life, and about being hurt more than he already has been. It's actually resulted in a strong emotional vulnerability in him, something most characters don't catch in his domineering and unsavory behavior. He tries to reign his feelings in and remain indifferent, but they slip easily. He claims not to care about the Order and what it does, but when Bak just brings up the project Kanda's expression changes from irritated to genuinely upset. Like, sad upset. Like kicked puppy upset. His anger is also something that slips through, it's just something he doesn't have as much of a problem expressing. Kanda's emotional buttons are easy to push and make him writhe inside, and he can't handle that kind of pain as easily at the physical attacks he can blow off like they're nothing.
Kanda's view of himself is a bit different compared to his actual behavior. Despite his pride, he regards himself as little more than a tool. He doesn't consider his life to have a lot of worth to it, and lives for the sake of others rather than himself (really, he lives for the sake of That Person. He's fulfilling his promise for her, not for himself). Despite the fake body he's in, he does regard himself as human. He makes no distinction between his past and second lives and considers all of them as himself. He doesn't think he's a good person, or that his behavior is or needs to be justified. It's just how he is, and he's not introspective enough to look beyond the surface value of it. He's apathetic about his own life except for living to keep his promise, throwing it around carelessly often to save the lives of other people instead of himself.
Despite all of the negative traits he portrays, Kanda actually does have a few close friends, people he genuinely cares about (To date, known to be Lenalee, Komui, Marie, Daisya. Alma is a special case as he was only a friend back in his childhood). And there is a noticeable difference in the way he treats them compared to everyone else. He's calmer, more civil, more agreeable, and even a little more open. He holds them with more respect and doesn't treat them as indifferently as finder #128 or the girl on the street who's busy ogling him. He doesn't treat them with contempt like the members of Central or the Noah. He's not touchy-feely or very open with his attachment, and he's still rough around the edges with them, but for the most part he treats them well enough. He doesn't have a reason to pretend to hate someone he doesn't actually hate, nor does he hide it, though even they can set off his temper and end up on the receiving end of his attitude. He lets Lenalee come to him for comfort when Leverrier's around, he's clearly upset by Daisya's death, and even Allen and Miranda notice a difference in the more open, less antagonistic way he talks to Didi about Zhu.
There's also his relationship with "That Person". He loves her, surprising as that may seem for Kanda. The first of his memories to return to him (and what may be his only memories to return to him) are the promise he made, and the feelings he felt about her. He's even reaching out in the memory of his dying, saying "I love you, forever". They're intense feelings, and despite the amnesia Kanda feels them just as much as he did then, if that he can't remember why. She's important to him, that he'd dedicate his whole life goal to keeping just one promise for her, and finding out the reality that she's his best friend doesn't turn him away. Alma as That Person is the one thing he's shown to put above his job. He may cooperate with it, but he won't let it get in the way of his one bit of hope, of happiness, if running off to get Alma out of the situation to die in peace is any indication, or even that he would possibly have a relationship with her despite their situations in a difficult war where they could die very easily.