[1] The speaking subject can be considered the father of his speech. The father is the origin and cause of logos. Derrida's criticism is centered on this idea. It would imply that the father resides outside of language. 'The father is not the generator or procreator in any 'real' sense prior to or outside of all relation to language ... it is precisely logos that enables us to perceive and investigate something like paternity. If there were a simple metaphor in the expression 'father of logos', the first word that seemed the more familiar would nevertheless receive more meaning from the second than it would transmit to it ... Living beings, father and son, are announced to us and related to each other within the household of logos' (Dissemination, p.80-1). The idea of a father preceding his son cannot be maintained with respect to a text that is preceded by a speaker because he is not outside of language. We should not conceive of language in the light of a comprehensive 'fatherly' instance that produces, governs, and directs it. It is precisely language that first enables this kind of thinking and such concepts as father and son; we are always already in logos.
Derrida shows that the father needs logos to be able to appear at all. Without the presence of a supplement, the origin cannot appear, which means that the supplement, logos, needs to precede the origin, the father. Thus, the hierarchical relationship between the father and his son is reversed. Everything begins with the supplement. Everything begins with the play of differences that makes the sounds and meanings (that makes the difference between 'father' and 'son', or 'logos'). But this play of differences in speaking is the same as the play of differences in writing. So why not say that speaking is like a form of writing?

[2] In Plato, Derrida and Writing, Jasper Neel argues about how Plato (who says not to write at all) defines himself in writing and that he knows he has to do so in order to be 'heard'. Although he condemns writing, he cannot escape it.
Plato condemns writing as a derivative and dead repetition of the living spoken word. This is what Plato leaves us with after Phaedrus. He is free to devalue writing because he has exempted Phaedrus from writing by making it dialectic, writing's privileged opposite. Plato can be considered the pharmakos who guides us out of the morass created by writing, and into the realm of truth.
But he leaves us with what he himself leaves: a divided, diseased inscription. What happens if we choose not to read Phaedrus as dialectic, but to call it what it is, writing? Plato wants to give us truth, but he cannot. He has to replace it with what it is not, namely, writing: 'What seems like a dialectical movement toward truth in his dialogues is really a written text whose end is known at the beginning and whose every aspect is managed through the revisionary, recursive process of writing' (Neel, p.70). Plato's desire is to escape writing through writing; and the harder he tries to master writing in writing, the more he is caught inside writing. Such platonic ideas as truth and soul find themselves in writing. Plato's Socrates describes them as the opposite of writing, but he has to describe them in writing.
What makes Plato important in history is precisely his writing so that his ideas remain open for all time. Plato's writing is revolutionary because he represents the invention of a literate culture in the middle of an oral culture. Plato knew Platonism was only available through writing. He knew that all Socrates speeches were preceded and enabled by writing. Dialectics was enabled by writing.

[3] Socrates dismisses writing as nothing more than amusing play. Plato succeeds in escaping from writing if we accept Socrates' devaluation of writing. But was writing really a trivial pastime for Plato? We know that Plato himself constantly revised his dialogues. Writing for him was a very serious, if not the most serious, affair. In fact, one could say that he was addicted to it. Writing was his pharmakon; it was a poison to him because writing turned out to be using him, and it was a cure because he loved what it allowed him to do. The source of his sickness was the source of his life (cf. Neel, p.56-78).