Something I find really interesting about Shadow Milk Cookie is that how..wishy-washy his 'embracing' of deceit and 'rejection' of truth is.
Do not get me wrong, Shadow Milk Cookie does embrace deceit, he is The Beast of Deceit after all, but I often simultaneously get the impression he loathes Deceit. There is so much constant bubbling resentment that infects almost every major Shadow Milk Cookie scene toward deceit and toward the fact that cookies as a whole are foolish and monstrous enough to prefer it to true Knowledge. He does not see Deceit as The True Way, he does not see Deceit as Good, not really, he sees it as a fucking tar pit that ruins every cookie who has ever lived selfish and broken enough lives to seek it out. Shadow Milk Cookie himself embraces and uses deceit because..it feels safe. It offers a measure of control. Shadow Milk Cookie uses deceit himself to protect himself with layers of masks, and the bitterly force others to choke on the Deceit they so love. I think Shadow Milk Cookie silencing the Light of Deceit is also very telling.
On the other hand, Shadow Milk Cookie's problem with Truth often feels less like the kind of deep bitter Hatred he often has for Deceit, and more of a source of pain? Truth is naive, Truth is not valued by cookies, being Truthful will get you hurt, if you throw your lot in with Truth you will inevitably realize your naivety the hard way when cookies break you apart for it with their greedy hands and distrustful deceitful hearts. Shadow Milk Cookie utilizes Truth at times, it's pointed out in canon that there are often bits of Truth in his Deceit, and there are several moments where he- while he buries it in layers of denial and symbolism because vulnerability scares him- is remarkably candid with Pure Vanilla Cookie about why he is the way he is when asked for understanding.
Truth is not bad, but prioritizing Truth as an ideal is naivety that it will get you hurt and break you into pieces.
Deceit is monstrous, and Shadow Milk Cookie loathes it, but to be monstrous is to be safe.
Then there's the ever looming presence of Knowledge, and Shadow Milk Cookie's continuing relationship with Knowledge is fascinating. It's obvious he is still strongly connected to The Fount of Knowledge. He has a statue of The Fount of Knowledge in the spire, during his Dominion of Beasts segment he is physically represented by The Fount of Knowledge's sprite at one point despite being labeled as (and obviously speaking as) Shadow Milk Cookie which isn't something he comments on (as if it is not abnormal to be internally represented as such), in chapter fourteen he willingly draws upon memories of being The Fount of Knowledge to show Pure Vanilla Cookie, he internally refers to himself as The Fount of Knowledge (among other things) in his internal monologue in chapter fifteen, and later in chapter fifteen he is haunted by "You don't know anything, Fount of Knowledge, so why are you The Fount of Knowledge?", which strangely indicate a strong continuous identification with a self one would think Shadow Milk Cookie would be much more invested in erasing.
And that last part, that question he is haunted with- "You don't know anything, Fount of Knowledge, so why are you The Fount of Knowledge?"- ties very strongly into Shadow Milk Cookie's intense continued desire for Knowledge. He is constantly asking himself questions internally, and is still strongly driven by that one big question he's been yearning after for thousands of years; why did the witches create him to fail, where did they go, and what could it possibly take to draw their attention? He is not so intellectual about it now, but the obsessive question, the search for Knowledge, remains. We're led to believe Shadow Milk Cookie abandoned the part of himself that cared for Truth and Knowledge when he split off a part of his soul into The First Headmaster. And perhaps he did, to a point, because Shadow Milk Cookie's love of knowledge and trust in Truth have long since rotted within him.
But despite the massive shift for the worst taken when Shadow Milk Cookie became The Beast of Deceit, I don't think his inclinations are quite what one would assume. Shadow Milk Cookie follows Deceit, but that does not mean he doesn't hate and resent it to the core of his being. Shadow Milk Cookie dismisses and distrusts Truth, but that does not mean he holds no inclination toward it. Shadow Milk Cookie is no longer The Fount of Knowledge, but that does not stop him from thinking of himself with that old name long after shedding it, from envisioning himself internally as The Fount of Knowledge without question at times, from grieving and resenting that he could never have fulfilled the duties of Knowledge, or from clawing at scraps of Knowledge desperately even now.
All of which is really really deeply fascinating to me and not something I think gets enough spotlight in fanon discussions of Shadow Milk Cookie.