There are a number of psychoanalytical theories attempting to explain to explain the phenomenon of cross-dressing, though I do not intend to investigate all of them because:-
(a) I am not familiar with them all,
(b) even if I were, it would take too much of my time to do so here in any event, and
(c) I don’t think that any of them I have encountered are sufficiently persuasive or substantiated by enough concrete evidence (if any such evidence at all).
Furthermore, even Harry Benjamin, a doyen amongst “sexologists” and founder of the Harry Benjamin International Dysphoria Association has stated in his book The Transsexual Phenomenon (1996) that:-
“...psychoanalytic theories are something like a cult, if not a religion, and are often quite incomprehensible to ordinary clinicians. To them, their explanations and analyses many times appear far-fetched, even absurd, in spite of their often intriguing and sometimes poetic quality…These psychoanalytic concepts have been accepted variously as important scientific discoveries, or as ingenious theories, but have also been criticised and rejected as merely intellectual "games," a sophisticated voodoo, if not as plain nonsense and balderdash...The prominent psychiatrists and university professors Buerger-Prinz, Giese, and Albrecht in an important German monograph [Zur Phenomenologie des Transvestismus bei Maennern.(1953)] call some psychoanalytic theories "think possibilities without evidence in clinical observation" (phenomenology).”
Having said that, I have commented on some of the theories I am familiar with, and more details of these can be found on the pages entitled Autogynephila, Perversion, and The Five Steps, respectively.