Case in point: For some reason that's not entirely clear to me, people find it useful to think about social relationships as though they were thinking about geography: "I'm closer to Timmy than I am to Tommy." The distance metaphor breaks down once you enter the realm of social relationships involving more than two persons: The geographical distance from A to C cannot be larger than the sum of the geographical distances from A to B and B to C. This is not true, however, for social "distances". Failure to understand this is the source of much misunderstanding.
Models are wrong because they abstract away from reality. If they didn't they wouldn't be models, but the actual things. They can be useful because they describe some properties of the real things accurately enough. There are also properties of the real things they don't describe accurately enough. The trick is to notice when you leave the realm in which the correspondence of the model and reality is high. This isn't all that easy because you're thinking not in terms of reality, but in terms of the model.