tl;dr: The Enneagram is a neatly structured theory and it has a lot of interesting insights, but it doesn't always work very well as a system. I've been thinking about this stuff a lot recently so I took this opportunity to write and post my thoughts. I know it's a ridiculously long post, and I won't be offended if no one reads it all, but I'm posting it all anyway in case it's of interest to anyone.
1.) Why is the enneagrams enneatypes placed the way they are? For example, why is an enneagram 7 placed in between 6 and 8? Why are the integration and disintegration points so impeccably positioned so that they form along with the other points, the entire geometric pattern and why does, for example, a 6 only integrate to 9 and disntegrate to 3? What is it about a 6 that gives off the impression that when they become 'disintegrated' they take on the traits of an arrogant and competitive spirit? Why does the enneagram 6 have a wing 7 or wing 5 and not allow a combination of say enneagram 2 or 4? What is it thats in the 6's DNA that makes them either a bit more intellectual or gluttonously fun?
The placement of the types is not arbitrary. As you probably already know, the types are divided into image/heart/shame types (2, 3 and 4), head/fear types (5, 6 and 7) and gut/instinctive/anger types(8, 9 and 1).
Those types are placed together because the types within each group supposedly share similar themes/issues based on the core emotion that motivates them, and the "center of intelligence" they operate from. You may also be familiar with the Hornevian/Freudian triads: assertive/aggressive/id (3, 7, 8), withdrawn/ego (4, 5, 9) and compliant/superego (1, 2, 6). If you look at how they are structured, you may notice that 1) in each of the head/heart/gut triads, there is one type from each of the Freudian groups, for example, the head triad has 5, an ego type, 6, a superego type, and 7, an id type, and 2) where two adjacent types don't belong to the same head/heart/gut triad, they belong to the same Freudian group, for example, 1 is a gut type and 2 is an image type, but both are superego types. So, if you are a 4, for example, you can either have a 3 wing, which reinforces the image issues, or a 5 wing, which reinforces the withdrawn issues. It gets a bit more complicated with the primary types because both of the adjacent types belong to the same triad, but I believe it's explained by the idea that each triad has
an inwardly focused type and an outwardly focused type, with the central type being both inwardly and outwardly focused. For example, 6s are both, but a 5 wing reinforces the inwardly focused side while a 7 wing reinforces the outwardly focused side.
So it's certainly an elegant theory, but does it actually work as a system for describing real people? Well, if we assume that head/heart/gut and id/ego/superego are the most significant divisions between the types, it makes some sense to assume that most people's secondary type will be one that has one of those groups in common. But that raises more questions than it answers; why should we assume those are the most significant groups? The types in each of the head/heart/gut triads are conceptually linked, but I don't think they are meaningful groups in terms of having personality traits in common. What does it mean to be, for example, a gut type? that you are motivated by anger? That applies to 8s and 1s, although in very different ways, but applying it to 9s is stretching it. That you are focused on the boundary between yourself and the outer world, and WTF does that even mean? That you have strong personal boundaries? So do 5s, and 9s generally don't. In other words, if I said, "My friend John Smith is a gut type," would that give you much of a sense of what he's like? I think not. I do think id/ego/superego are significant groups, although I think it's better to view id/superego as a dichotomy (like MBTI's J/P, although some I/E stuff has got mixed up in there) and withdrawn-ness as a separate thing, essentially introversion (although it probably applies better to INs than ISs).
Even if we assume they are significant groups, why couldn't a 1, for example, have an 8 wing (since they're both gut types) or a 6 wing (since they're both superego types)? How do we know the types are correctly placed? For example, 1s tend to identify with their minds, are often intellectual (especially 1w9s) and Sp 1s, (according to Naranjo, I think) are often more anxious than 6s, so there's a case for putting 1s with the head types; even Riso and Hudson say 1s tend to think of themselves that way. Meanwhile, 7s are a much more physical type who, like 8s, enjoy the pleasures of the senses. Many of them like their activities to be intellectually stimulating, but I don't think that's a core part of the type. They tend not to be very anxious (they fear being trapped and in pain, but all the types have a basic fear) so that's not a good reason for classifying 7 as a fear type. As for the Freudian groups, Naranjo talks about the "high super-ego" of 5s, and he portrays 2s as an id-ish/hedonistic type whose giving is about being seductive, rather than out of a sense of duty, or to earn love, as you'd expect from a superego type (and from the way sources like Riso and Hudson describe them).
As for the dis/integration points, if you divide 1 by 7 (7 being, of course, 1's integration point) you get 0.142857, and as you've probably noticed, that's the sequence of disintegration points. So I think it's another case of it being an elegant theory that doesn't necessarily apply all that well to real human psychology. A few of the dis/integration points make sense, but mostly I don't think it adds much to the theory. I believe the thinking among some people is that the patterns in the Enneagram symbol apply to human personality because they apply to any system or process and capture the inherent order within the universe. I'm sceptical of that.
2.) What do you make of your enneagram type?
I've had trouble settling on one type, and I've started to think that's mostly because of the discrepancies in the ways that different authors describe the types. There are several that accurately describe something about my psychology, but all of them have some key trait that I don't relate to (a trait that, according to some people, if you don't relate to it, you're not that type). I've mostly been flipping between 1 and 6. 1 because I relate to the perfectionism/criticality, inner critic, the sense that things are never as they should be, inability to accept my own mistakes, strong convictions, ETC, and I really relate to what Palmer says about how 1s pay attention. What I don't relate to is reaction formation. I can't think of a single example of a time when I've done that. And yet, the entire type 1 personality is a reaction formation against anger. Also, I don't relate to those SJ-ish descriptions saying that 1s are obsessed with neatness, manners, social conventions, ETC. Although some sources say that whether any particular 1 even cares about those things depends on their own individual standards.
For type 6, I've found that some profiles of the type describe me really well, and others are totally off. I'm not just talking about having a couple of traits that I don't entirely relate to, I mean that they're pretty much the opposite of what I'm like, what I value, ETC. Typewatch's 6w5 description is one of the best descriptions of myself I've come across, but most of what Riso and Hudson say about 6s is not me at all. Maybe that is to be expected, because of the phobic/CP distinction, but I don't really relate to either side of that dichotomy. I am far too cautious to be CP, and I don't relate at all to the idea of doing things that scare me to prove I'm not afraid or throwing myself into action when I'm anxious, but I also don't relate at all to the phobic descriptions about "warmth" and submitting to/wanting to be protected by some authority. On the other hand, the anxiety, worst case scenario thinking/contingency planning, not easily trusting and wanting open and clear agreements, dislike of uncertainty/ambiguity/unpredictability, even the "yeah, but..." way of thinking, I relate to completely. My way of thinking, and many of the assumptions I make about the world, seem very 6, but I don't relate to the 6's authority issues.
At one point I typed myself as a 5, and I can't entirely remember why I decided I couldn't be that type. It might have been because I relate to the compliant/superego group (when the descriptions aren't too SJ-ish, anyway). I relate to the withdrawn triad too, but lots of introverts mistakenly think they're withdrawn types, so they say. It might have been because I thought I wasn't detached enough (I've read quite a few forum/blog posts from people who are knowledgeable about the Enneagram, talking about someone who thought they were a 5 because they were introverted, intellectual and emotionally detached, but still weren't detached in the same way 5s are). Also, I don't think I have the pattern over my life that 5s tend to have, of avoiding obligations. However, I do relate to the search for knowledge, the strong need for privacy, the hoarding tendencies (I think; I don't collect things, but I do tend to hold on to things I haven't used for a while because of a vague sense I might need them someday), even the 5s attraction to/fascination with what disturbs them. I think there's a bit of 4 in me too, but I'm quite sure that's not my core. So I still take an interest in the Enneagram because I think it's got some insights the MBTI has missed, but there are a lot of intelligent, self-aware people who can't figure out their type, and that makes me think we probably don't all fit neatly into one type. Tritype isn't an entirely convincing solution because of what I said about head/heart/gut not being particularly significant groups.