Lacan's concept of the name of the father and a central signifier of thesymbolic order which replaces the mother as object of desire, leaving a persisting sense of absence, is one of the keys to understanding Lacan's subject theory and why he thought it was constructed of and as language. Through the name of the father the baby enters the realm of signification which constitutes him as a subject. Repressing the Oedipal complex is done through the name of the father, that is language, and this for Lacan means that the subconscious is constructed as language.
To understand the why Lacan argues that the subject is, in a sense, language, we can use the example in which Lacan draws on the work of Roman Jakobson regarding metonyms and metaphors and how he compare them to mental processes in the unconscious like conversion and displacement.
According to Lacan both conversion (the metaphoric function) and displacement (the metonymic function) point to the fact that language itself as an inherent resistance to meaning. According to Lacan, the stable link between signifier and signified, required for the use of language and the construction of the self as a coherent category, is produced by the function of the imaginary which allows for the assignment of signifiers to signifieds and thus limit the endless shifts of signification.
Assigning a relatively fixed signifier to a signified as what enables us to have a relatively coherent sense of reality and of ourselves, and without them Lacan warms that the subject might be "lost" (in two senses) and turn psychotic. On the other hand too many fixed signs might produce fixations in our lives which will deny us the ability to grow, develop and give new meaning to our existence, leading to all sort of mental and emotional problems.
Lacan stresses that the gap between signifier and signified can never be fully bridged, and never fully described or understood. This gap points to the eternal divide between the person speaking (the "I" or "self") and the one being spoken about (the unconscious subject). In language, according to Lacan, we turn alienated from ourselves for the sake of being able to communicate with others.