Like the early sexologists, Freud believed that women were sexually passive, engaging in sex only because they want children. Because they do not have a penis, girls come to believe they have lost theirs, and eventually, seek to have male children in an attempt to “gain” a penis. Penis envy in women is a problem that Freud believed could never be completely resolved, thus condemning all women to underdeveloped superegos, implying that women will always be morally inferior to men, who are capable of having fully developed superegos (Schultz & Schultz, 2009). For someone whose theories are centered on sex, Freud seemed content to remain willfully ignorant of female sexuality and how it may differ from male sexuality.

Karen Horney, a psychoanalyst who broke away from Freudian theory, criticized his work, particularly his theory of penis envy. Freud never directly responded to Horney’s criticisms, though he called her “able but malicious,” and wrote of female psychoanalysts, “We shall not be very greatly surprised if a woman analyst, who has not been sufficiently convinced of the intensity of her own wish for a penis, also fails to attach the proper importance to that factor in her patients” (Schultz & Schultz, 2009).

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Lacan:

Nowhere does it appear more clearly that man’s desire finds its meaning in the desire of the other, not so much because the other holds the key to the object desired, as because the first object of desire is to be recognized by the other. (Lacan, 1977 [1959], p. 58)
That the other holds the key to the object desired takes on added value later in Lacan’s work. Yet that desire emerges in a relationship with the other which is dialectical, that is, which is embedded in discourse, is an essential property of human desire. Human desire is the desire of the Other (over and above the others who are concrete incarnations of the Other), not ‘natural’, endogenous appetites or tendencies that would push the subject in one direction or another irrespective of his/her relations with the Other; desire is always inscribed in and mediated by language (cf. The Four Fundamental Concepts of Psycho-Analysis, which is an essential reference in its entirety; Lacan, 1977).

Lacan’s study of the dialectical nature of desire led to his distinction between desire, need and demand. The three terms describe lacks in the subject; yet it is indispensable to identify each of these lacks, and their interrelations. The satisfaction of vital needs is subject to demand, and makes the subject dependent on speech and language.

The least noisy appeal of the infant is already inscribed in language, as it is interpreted by the ‘significant’ others as speech, not as a mere cry. This primordial discursive circuit makes of the infant already a speaking being, a subject of speech, even at the stage in which he/she is still infant. This subordination to the Other through language marks the human forever. Lacan writes:

The phenomenology that emerges from analytic experience is certainly of a kind to demonstrate in desire the paradoxical, deviant, erratic, eccentric, even scandalous character by which it is distinguished from need […]
Demand in itself bears on something other than the satisfactions it calls for. It is demand of a presence or of an absence — which is what is manifested in the primordial relation to the mother, pregnant with that Other to be situated short of the needs that it can satisfy.
Demand constitutes the Other as already possessing the ‘privilege’ of satisfying needs, that is to say, the power of depriving them of that alone by which they are satisfied […].
In this way, demand annuls (aufhebt) the particularity of everything that can be granted by transmuting it into a proof of love, and the very satisfactions that it obtains for need are reduced (sich erniedrigt) to the level of being no more than the crushing of the demand for love.
Thus desire is neither the appetite for satisfaction, nor the demand for love, but the difference that results from the subtraction of the first from the second, the phenomenon of their splitting (Spaltung). (Lacan, 1977 [1959], pp. 286-7)
This residual status of desire constitutes its essence; at this point the question of the object of desire acquires crucial importance. Lacan considered his theory of this object to be his only original contribution to psychoanalysis.

Although an exaggeration in reality, Lacan’s position is justified because with that theory he introduced in psychoanalysis a conception of the object that is genuinely revolutionary and that makes possible a rational critique of the notion of ‘object relations’ and its clinical applications.

For what Lacan emphasized was the illusory nature of any object that appears to fulfil desire, while the gap, the original splitting which is constitutive of the subject, is real; and it is in this gap that the object a, the object cause of desire, installs itself. (Lacan 1977; in particular, chapter 20).

Desire requires the support of the fantasy, which operates as its mise en scène, where the fading subject faces the lost object that causes his/her desire (Lacan 1977 [1959], p. 313). This fading of the subject in the fantastic scenario that supports his/her desire is what makes desire opaque to the subject him-/herself. Desire is a metonymy (p. 175) because the object that causes it, constituted as lost, makes it displace permanently, from object to object, as no one object can really satisfy it.

This permanent displacement of desire follows the logic of the unconscious; thus Lacan could say that desire is its interpretation, as it moves along the chain of unconscious signifiers, without ever being captured by any particular signifier (cf. Seminar VI, ‘Desire and its Interpretation’; Lacan, 1958-59).

In the analytic experience, desire ‘must be taken literally’, as it is through the unveiling of the signifiers that support it (albeit never exhausting it) that its real cause can be circumscribed (Lacan, 1977 [1959], pp. 256-77).