They fuck you up, your mum and dad.
They may not mean to, but they do.
They fill you with the faults they had
And add some extra, just for you.
-Philip Larkin, This Be The Verse
Not the facile pop-psychology I was expecting, rather a book with some penetrating insights. As other reviewers note, "gifted" in this context does not refer necessarily to academic or artistic gifts (though these are common in the patient group Miller describes), rather a kind of emotional sensitivity.
Briefly, Miller describes the narcissistic personality disturbance. Here narcissistic is used not in the broad sense of vain, being in love with yourself etc. This narcissism is an internalisation of the great expectations of one's parents, the consequent lasting feelings of inadequacy and drive to greater and greater successes (that leave one hollow). Narcissus did not fall in love with himself, but with a false reflection of himself.
The twin manifestations of narcissism are grandiosity and depression. Each is a defence against the other. Grandiosity arises as a person feels their achievements render them superior to everyone else. Depression strikes when they realise they will never achieve as much as "necessary" to support their ego, or that all achievements are empty. Both these manifestations can be traced back to a failure to express one's true self and an idealisation of a false-self instilled by parental desires, pride, ambition, vicarious status-seeking etc. Grandiosity is characterised by contempt for others (who have not, as a casual example, read as many books or displayed as brilliant intellectual and artistic accomplishments). Depression is characterised by contempt for oneself, when one does not (cannot) meet one's own expectations. Anything less than world-historical greatness (and perhaps even that) is seen as failure, that is, pathetic mediocrity. Notably, parents do not have to be physically abusive to have these effects. A small child, entirely dependent on its parents for all its needs, will do anything to ensure their attention and will take careful note of the smallest expressions of admiration or derision. Thus a keen sensitivity as a child instils a cripplingly powerful super-ego.
Miller claims that the key to these feelings is the realisation that one was loved as a child not for who one was, but (in large part at least) because of one's achievements. This leaves the child always desperate to achieve more, to safeguard their parents' love. One's own personality, desires, needs and emotions are suppressed to create a projected perfection which attracts love and awe. Recognition of this allows the patients to be who they are for the first time and to experience their own emotions - both positive and negative. It is remarkably difficult for some people to even contemplate negative thoughts towards their parents. Childhood memories of abuse are among the most strongly suppressed or displaced. Miller references Ingmar Bergman who described in great detail the violent abuse his brother faced at his father's hands, but had no recollection of any mistreatment to himself. (Of course, it seems rather unlikely that he went through his childhood entirely unscathed).
This is all pretty simplified, the book is brief and well worth reading particularly if you see aspects of yourself or someone you know in the above. Though some of the book passed me by there were sentences that gutted me like a fish...
As I look forward to becoming a parent myself within the next few months (against Larkin's advice, if you know the rest of the poem) I can only hope to not fuck up my child, or at least to fuck them up as little as possible. That is, to avoid projecting my own desires and fantasies and personal conception of success onto them and to allow them to flourish as their own person.