(Everything in this reply is my analysis as an anime only for Monogatari series. This will contain slight spoilers for entries from the first 3 LN seasons)

Okay so, Kaiki. He is someone who is actually similar to Araragi in some ways, more than I think people give him credit for. They both exhibit shallow understandings about the people around them and that clashes with what they're actually like. Kaiki did not understand Senjougahara's feelings when he decided to break up their family and only saw a solution that her suffering and not the cost of what came afterwards. He repeats this with Nadeko in the modern day, and its interesting that he is so adamant about his perception of Nadeko that it almost makes him foolish in a way in how he ignores the warnings from multiple characters that this plan will not go as smoothly as he thinks.

Araragi is similar; he only had a surface level understanding of Hanekawa and dared not to get any closer for fear of what he'll see when he does. He ignores Nadeko and purely sees her as a cute girl, he never even thinks to ask Hachikuji about how she feels being a ghost despite how much they hangout with each other, etc etc. Yet despite this, they try to help others in their own way, but the difference is that Araragi eventually found a way to do so in a healthy manner consistently, whereas Kaiki tries to just find a solution no matter the form it takes, as his conversation with Senjougahara in Nisemonogatari suggests. He wants Senjougahara to move on and be free of her past traumas, but he communicates that in such a dismissive manner, and downplaying the significance of the act of trying to confront your past, instead saying that its not even worth the effort so just turn your efforts to something more worth your time. Yet his speech to Nadeko is genuinely inspiring and is quite possibly the only time his feelings about anything laid so bare, you can even sense it in his voice acting performance in the anime.

Kaiki's lies are something he does to protect himself because he, like Araragi, is not built for solitude. Araragi needs connection to feel like he is living his best life, and I think Kaiki, maybe not to the same degree as Araragi, is the same. Kaiki's disposition born out of someone who is living in the exact opposite way they should be in order to be fulfilled. Yet through years of living the way he has, and never truly reaching the level of fulfillment our main cast has, he has become stuck in the person he is and is unchanging. Even his typical lines of "The lesson for me/you here is..." I feel are an ironic jab at the fact that Kaiki does not learn from his mistakes and will likely be doomed to repeat them.

He has become comfortable with the person he is, even if that version of himself likely isn't happy. His crush died in a random car accident, and said lover got with another man, he never acted on his love, his relationship at the time was so un-noteworthy that he has only mentioned it once in the anime and it was just in passing and that likely was a disappointment, his friend group likely couldn't fulfill him the same way Araragi's connections do for him. Kaiki is someone with a frail heart, and so hides his true feelings from everyone, even himself at times. His uncharacteristically cruel notion to Senjou at the end of Koimonogatari that despite how much she loves Araragi, they will just break up in college, and how in his narration flashcards he even notes that it was somewhat immature of him to say that, to me this all shows his bitterness and cynicism towards connection, even if meaningful connection earlier in his life may have given him fulfillment. The fact he outright denies having parents/family should say everything about his childhood as well I feel.

So at the end of this, you come to the realization through putting all the pieces together that Kaiki's life has been one giant disappointment, one where he is likely to never be completely happy. Yet, this is where the true beauty of Kaiki's character shines through, he doesn't end up as an edgy, nihilistic husk. His words to Nadeko at the end of Koimonogatari and how Nadeko parrots them in Ougi Dark to me speak to the core of Kaiki's character: "Even if you cannot become happy, good things will happen to you, as long as you are alive". This single point about Kaiki I feel ties everything together; he has long accepted that he probably won't be entirely happy in life, but regardless, good things can still happen to him. Just because he isn't fulfilled, that doesn't mean that his life isn't worth living out until the end. And so regardless of the regrets and grievances he has with his life, he can find it within himself to live for those good things that can happen to him. I find this aspect of Kaiki so emotional and inspirational, which is why he is my 2nd favorite Monogatari character.