While You Make Some Great Points I Think You're Overlooking Some Aspects Of His Character - I Don't Think

While you make some great points I think you're overlooking some aspects of his character - I don't think either of these voice lines are a part of his facade, and are in fact both a result of it being broken.

X indeed likes to be, or be perceived to be, in control of a situation. You explained this really well and made some points that I didn't even think of before, so I won't touch on this.

X likes to project an image of a goofball, a silly fella, little guy. Someone who is aloof and careless. We can see this in his placing of newspaper clippings in a prominent places of his cabinet in his second story (Something for nothing 40%) - the second headline where he is called a "Foolish Genius" is placed just as prominently as the previous one praising him.

Neither of these responses to being hurt allow him to retain this image very effectively.

I think that he's surprised by being hurt and that breaks through his mask. The second voiceline is indeed probably a more controlled, less vulnerable response, but that doesn't mean it isn't also genuine.

We know that X is very calculating. He's a genius and likes to plan around situations, manipulating chance and other variables in his favour. In Laplace/the suitcase this means inventing new things (and getting praised for it), testing his machines on/with people, being helpful and having mischief/adventures with his friends.

We also know that he can also have pretty violent tendencies and that he killed someone whilst at the orphanage (presumably an abusive caretaker).

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From the interview with UTTU in his story: Life Is Filled with Surprises (80% bond)

Pandora Wilson: Please introduce this exquisite mechanical ball you're holding.

X: It's just a toy I made for fun. Instead, I'd like to introduce this Auto-Seduction Lipstick I've just invented. Have a look! Is there anyone in the world better suited to test this out?

Pandora Wilson: That's alright. What an impressive invention.

Pandora Wilson: Let's talk about something else. There was an accident at an orphanage a few years ago and I heard you were present.

X: Oh? If you want to discuss topics that have nothing to do with the interview, you have to test this Bubble Gum Spraying Alarm Clock in exchange, okay?

Pandora Wilson: The deceased appeared to have been killed by a loose shingle from the roof. The angle, wind speed and power it had was incredibly precise.

X: Oh, such is life. It's filled with coincidences and accidents.

X: Don't be sad. Now, let's try this Mini Priest Bouncer and pray for him, shall we?

Pandora Wilson: Please excuse me.

X: ～♪～

Pandora Wilson: Ouch! Don't pull me!

X: ～♪～

Pandora Wilson: ...♪

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He refers to any casualties in battle as an accident in voicelines and claims that there are no such thing in others.

He's also been stated to be a hitman by a Twitter post from the developers, but whether this is outright stating that he worked as an assassin or just a translation issue or metaphor, I don't know (It is also in several places of the wiki, but I'm not too sure on the sources for these).

His Green Lake garment described him as being the perfect killer and that all the cases go unsolved (though how cannon this and the other garments are I'm not sure, so take it with a pinch of salt).

Fortunately this is supported by his Portray/Artifice description: Sometimes, he has to shed some blood for the sake of others. Fortunately, he has machines to do that for him.

He doesn't want people to know about this violent part of himself.

I also think his use of the seduction lipstick is very interesting as it's his response to Pandora's persistence in her line of questioning when redirection fails. (Also did he just grab her and kiss her??)

Anyway I think the idea of identity, morality and choice are very central to X's character - can any actions be considered fake if you are still choosing to act in that way?

From an item description for the Green Lake garment:

A broken white mask that likely came from a corner store having a Halloween sale. The respondent raised a question with a smile: "Does the mask need the face that wears it, or does the face need the meaning the mask gives it?"

Very very disorganized X thoughts

Based on mostly voicelines

His incoming lines make me think a lot, honestly

X is a liar, as it's stated several times in-game. He hides in his Goldberg machines and creates his own reality for fun, and quite possibly to feel safe from the external world. All of his confidence shows in times where he knows he has the full control of the situation ("Haha... I got you! I won't let you go, unless you agree to join my experiment!"). He likes to push people into his own world, but he's also dependent on them; he needs people to show them his machines, no matter how much he tries to satisfy his own desires with his creations, if there's nobody to test them on or show them to, what's the point?

"Try my new inventions... Ah! I had never prepared for a plan B in your absence..."

"Can I borrow you tonight? I really need your help for my new machine... please?"

"It's so nice to meet you! I've been waiting for so long!"

So, despite the confident and self sufficient facade he likes to put on, X is constantly referencing and asking for the attention of those around him ("Please live up to my expectations, colleagues!" "Ah, I seem to have grown a bit taller recently. Can you tell?"). If he ever takes an "imposing" role, it's when he's 100% sure he has enough power to enforce it, and he does want to have that power and confidence permanently and don't depend on other people and the external world anymore ("The day I've waited for has finally come. Welcome to my world."; Bottom of Insight line).

He reaffirms everyone likes him although of his eyes, something that caused a lot of rejection from people his age ("My eyes.. a little scary, aren't they? Kids new to the orphanage were a little afraid of them, but in the end everyone likes me."), and possibly the adults in charge of them themselves. He's dealt with a lot of rejection and mistreatment since he was a kid, and he looks for validation constantly, hiding under fake confidence and acting rebellious and chaotic on purpose to reaffirm said facade. He references his orphanage quite often in his voicelines, only when he's talking to Vertin, a friend he presumably can trust.

Going back to his Incoming voicelines, the first one really sticks out. They're both completely different reactions to the same threat, and one if them is most likely an act. My point is: considering X's facade mostly consists on appearing capable of anything, in control and smarter and more powerful than other people I don't know why he'd pretend to be scared.

Given how he talks about the orphanage, being a place where kids weren't even fed enough, didn't have winter clothes, weren't even allowed to exit the building, how much he liked to cause trouble, even trying to scape once, and how orphanages were in that period of time, it's highly possible kids faced physical violence from the adults in charge of them. Imo, the first line is genuine. He's recognized a threat, he knows he lacks enough power to face it, and he's scared of getting hurt. The second one is just another attempt at looking like he's in control of the situation. As I've said before, these lines are specially interesting to me because he is in battle, where he isn't in perfect control of everything, that's not his world completely and he can't drag people into it like he does at Laplace, so it makes perfect sense that he drops the facade for a moment facing a real threat.

Maybe this was all really obvious but whatever. I like him a lot