A possible explanation for this is that more secure children come from higher income families(The textbook says that there are more secure children in middle class families than lower income families). It is possible then that more of these children from better off families go to college and get higher education, resulting in them being better off in life later on.
I agree with this, since families with higher income usually have the secure attachments, but they are also able to afford a better education for their children. Therefore, these children are more likely to be better off.