This is an interesting question, since Lady Brett Ashley spends most of the novel demonstrating that she does, indeed, lack self-respect. Most of what we see is evidence of this condition, however, rather than any long discussion or many thoughtful introspections about why she acts as she does.
Brett is the only significant female character in The Sun Also Rises by Ernest Hemingway, and she has connections, of one sort or another, to every male character in the novel. Undoubtedly she does not have a healthy respect for herself or her body.
Brett is "damned good looking" and has no trouble attracting men. In fact, every major male character in this novel claims to love her, or at least desire her. Just like the men, she smokes, drinks, and is never criticized for her provocative clothing or her promiscuous behavior. She is strong and independent in many ways, and we see that as she maintains the control in her relationships. Despite all of these things, however, she is clearly a lost and wounded soul who knows she is hurting others but is unmoved by this fact. She is careless of things (her cigarette ashes on Jake's rugs) and of people (too many examples to cite), which is a clear indication that she places value on nothing--including herself.
So, the question of what caused this kind of aimlessness and self-loathing is a good one, and it seems to me there are only two possibilities. First, she does seem to be trying to somehow recreate the experience and satisfaction she had with the lover who dies of dysentery, the man she calls her "own true love." Once she loses this, she spends the rest of her life trying to somehow recapture it. The closest she gets is Jake, I suppose, but of course it is not the same. This constant quest for fulfillment is an indication that something is missing, and it is this lacking thing, this fulfillment, which seems to be causing her self-hating behaviors.
The other possibility is connected to the first. Hemingway, of course, was part of what is referred to as the "lost generation." After World War I, things were changing and the traditional roles of men and women were being questioned, overturned, and reshaped. The lost generation was searching for both meaning and identity, and they turned to alcohol, sex, and other forms of pleasure to find them. Their excessive pleasure-seeking made things worse, of course, because it simply added to the confusion.
In this novel, it is clear that both Jake and Brett are representative of the lost generation. Brett seems to be the epitome of the modern woman, short hair and all; however, she is trapped by her own need to be in a relationship with a man. Even when things are going well, her misery is consistently just below the surface.
"Oh darling," Brett said, "I’m so miserable."
[Jake] had that feeling of going through something that has all happened before. "You were happy a minute ago."
It is clear that even in the one relationship which might give her love (though would certainly not fulfill her completely), she is not content.
The loss of the one man she loved is a hard blow for Brett and undoubtedly causes her to do things which do not demonstrate self-respect. This is a personal experience which clearly shapes her future behavior. Another contributing factor is the general malaise of not knowing quite how or where she fits into the post-World War I world, something which was not specific just to her. The combined effect is a dramatic display of self-loathing.