Is it a paradox that those with a lower level of self esteem are the ones who can be the loudest about their achievements? Perhaps not. When a person's achievements do not satisfy their need for self-importance, he/she may look to fill that hole with esteem from others. In this case, when internal motivators fall short, external motivators may be focused on too heavily.
So, this all makes sense to me. However, what does not make sense is the behavior which stems from the need. If the principle that people like to talk about themselves holds true, it would follow that the more you talk about yourself, the less likely it is that people are going to like to talk to you. Of course, if it seems not-well-thought-out, that's probably because it's not. In a sort of subconscious panic to gain attention and acceptance, people try the most proactive way they can in order to put themselves out there: talk themselves up (or sometimes even down). People talk more about themselves and their own experiences, putting them in a continuous downward cycle.
Conclusion: Talking about one's self can both be a fulfillment of a need and a detrimental reaction to a lack of fulfillment.
Experiment: For one week, I will direct conversation toward the other party as much as I can. I will ask questions, make encouraging comments, and be as interested as possible, but I will only tell stories or talk at any length about my own feelings on the subject if specifically asked. Hopefully, this will be beneficial in several ways: by strengthening my relationships with others, increasing my knowledge of others' experiences and feelings, and helping my discipline my own insecure behaviors. It's like fasting :D