A) Deficiency of empiricism: The senses cannot convey necessities, infinities, or whatever (the exact focus varies); and yet we can know things about these despite having no sensory basis for them.
B) Necessity of language: (A) is essentially an argument for rationalism, broadly speaking: there are truths we know independently of the senses. But the traditionalist opts for a weaker rather than a stronger version of rationalism: the human mind being what it is, our ability to think about necessary truths depends not on pure thought but on our ability to use and understand language.
C) Requirement of teaching: Language is not something that automatically comes to human beings; we must learn it from those who already have it.
D) Impossibility of infinite regress: This sets up a series of teachers: we learn language from our teachers, who learned it from their teachers, who learned it from their teachers, and so forth. But it is absurd to suggest that the series of teachers goes back infinitely.
E) Conclusion: Therefore there must be a first teacher, who did not need to be taught; and this all call God.
Arguments of this kind had a brief but widespread popularity in the nineteenth century; but one often only gets a gesture at the argument. To understand the argument, one needs to look at its most forceful and influential exposition, which is that of Bonald in the Preliminary Discourse to his Législation Primitive. Louis Gabriel Ambroise de Bonald (1754-1840) was a French statesman and is also considered one of the major figures in the early days of the field of sociology; the Législation Primitive was published around 1802. I've gathered below a few passages relevant to the traditionary argument. The translation is my own; as the passages were gathered from a first reading of the Preliminary Discourse and translated somewhat on the fly, I do not as yet vouch for strict accuracy on every point of detail.
Philosophy, which according to the pagans signifies the love of wisdom, and which signfies for us nothing other than the search for truth, began for man with speech, and for the world with writing.
***
The doctrine of the Hebrews revealed the cause; the philosophy of the pagans was stopped at the effects; Christianity came to reveal to the world the knowledge[connoissance] of the universal mean, medius, or mediator, of the being that unites the universal case to the universality of the effects, to the universe, and that forms the relation between the Creator and the creature.
***
These truths must be learned from men, if one wishes them to know them; and to speak to them the speech of God in order that they may have the thought of God...
***
This rational proposition: "Thought cannot be known save by its expression in speech" contains in itself all human knowledge [science], as the Christian maxim, "God is not known save by His Word" contains all the knowledge [science] of God, and for the same reason.
***
Speech is the natural expression of thought; necessary, not only in order to communicate knowledge [connoissance] to others, but in order to have the knowledge [connoissance] itself, intimate, that one calls having consciousness [conscience] of one's thoughts.
***
The solution of the problem of understanding can therefore be presented under this formula: "It is necessary that man thinks his speech before speaking his thought."
***
So the proof of the existence of a being superior to man, and of a law anterior to reason, is always equally strong; if one demonstrates that, given the operations of the human intelligence, and the necessary concurrence of his organs, it is impossible that man should discover speech and make a language, and that, far from having invented speech, man was not able, without speech, to have even the very thought of the invention.
***
It seems that one believes it more worthy of the grandeur of God to suppose that we receive thoughts immediately, and without the intermediation of a mean or milieu that realizes them and renders them sensible. Without doubt, absolutely incorporeal understanding could have ideas of this sort; but the organized understanding is but a mind in charge of helping a body: so that if it is thought, it, it must have been expressed; and God submitting himself, and more than that man, to the general laws that He has established, gave thought on condition of speech, as He has given vision on condition of sight, and hearing on condition of ear.
***
If the human race primitively received speech, as we have said above, it is wholly necessary that it has received, with speech, knowledge [connoissance] of moral truth. There is therefore a primitive, fundamental, sovereign law, a chief law, lex-princeps, as Cicero calls it, a law that man did not make and he cannot abrogate. There is therefore a necessary society, a necessary order of truths and of duties.
***
If language is of human institution, like the printing press and the compass, speech is not necessary to man in society; for nothing that man invents is necessary to society, because society existed before the invention. Domestic society itself is not more necessary to man, because the free agreement of father and mother for conservation of the child, presupposes will, thought, consequently expression, and if man invented speech, man invented, I do not say marriage, but family. Ad when I say speech, one must understand expression of thought, even by gestures, speech of those who do not have any other, of the deaf and the mute, but speech transmitted, like the other, by the interaction of men; for beasts have nothing of gestures, even though they have movements, and the blind do not have gestures, even though they have speech. Abandoned children, outsidof all communication with speaking men, do not make imitative gestures, even though they have animal movements, and given involuntary signs of pleasure, of sadness, and of desire. But in order to make imitative gestures, one must have seen actions to imitate, one must have observed that this gesture corresponds to this action, and consequently one must have lived in society with beings that think and that express themselves.
***
If speech is of human invention, there are no necessary truths, because all necessary or general truths are not known by us save by speech, and our sensations only transmit to us relative and particular truths. There are no geometrical truths; for how do I know, other than by speech and reasoning, that there are absolutely and necessarily straight lines, absolutely round circles, absolutely right-angled triangles, when my senses do not ever convey anything save relatively straight lines, and relatively round circles, etc., etc.? There are no arithmetical truths; for my senses see nothing save one, one one, and it is my speech that counts three, four, a hundred, a thousand, etc., etc., and which adds values that do not fall and have never fallen under my senses. There are no moral truths: for all these truths are not known to us save by forms of language that the inventor, free in his inventions, was able not only to invent, but to invent wholly different from those that exist today, and even different inventors in different people, for why is there but one inventor? There are no historical truths, and men do not know anything save what they see and what they touch, and, again, even if he knows the beings, he is not able to combine their relations, because he cannot combine them save by the aid of thought expressed by speech.
***
The uniformity of languages, in the sense that they are intertranslatable, and the same thought is understood by diverse people, inclines against the attributed invention by man. There is a general institutor who has given a general tongue, which was modified according to place, time, and person; as one and the same teacher of writing has given to a hundred students a different writing, according to the structure of their members and the liveliness of their minds, and as one hundred different figures of speech render one and the same thought, one hundred different writings render one and the same speech.