While there does seem to be some sort of correlation between the attachment style exhibited by a child and their well-being later in life, there are many other factors that contribute to how a child turns out as an adult, and therefore we cannot say that attachment styles cause certain attributes in adults. For example, it has been shown that those children that showed "secure" attachment styles grew up better adjusted and more able to socialize with people. However, it was also shown that the majority of children that were "secure" grew up in middle class or upper class families, so money or the types of neighborhoods that middle-upper class people live in could very well have a larger impact on how children grow up.
That's a good point about the child's socioeconomic status. A child who grows up in a poor family would seemingly experience more difficulties than a child growing up in a wealthy family. This difference in the number of struggles the child encounters could play a major role in determining both the child's attachment style and later well-being.