Exodus 34: 27 The Lord said to Moses: “Write these words for yourself, for according [literally by the mouth of] to these words I have formed a covenant with you and with Israel.”
Gemora Gittin (60a) Rabbi Yehuda Bar Nahmani said ‘One half of the posuk says “Write it for yourself” and the other half says “according to these words” [literally ‘by the mouth.’] How can these both be possible? The answer is: Written things [teachings] are not appropriate to be said aloud and Oral things [teachings} should not be said through writing’
Torah Temimah Colloquial Translation on Note #40:
In other words, both are true and the fact that the two phrases are attached as one teaches that this principle should never be overturned. The part that was given in writing is not appropriate to be said orally. And this that was given orally, it is not appropriate to write it.
It is not clear to me what Rashi means when he writes, “The teachings that I told to you in writing, it is not appropriate for you to give them to the Israel orally”. Why does Rashi explicitly mention not being permitted to give to Israel orally? Doesn’t this prohibition apply to each individual? Perhaps the explanation is related to the statement of God to Moshe that the purpose of saying the Torah is to teach it to Israel. This issue requires further study.
Many reasons have been suggested regarding this prohibition of not writing the oral teaching. The Rambam writes in the Guide for the Perplexed in the beginning of chapter 71, Part 1 as follows:
Even the traditional Law, as you are well aware, was not originally committed to writing, in conformity with the rule to which our nation generally adhered, “Things which I have communicated to you orally, you must not communicate to others in writing.” With reference to the Law, this rule was very opportune; for while it remained in force it averted the evils which happened subsequently, viz., great diversity of opinion, doubts as to the meaning of written words, slips of the pen, dissensions among the people, formation of new sects, and confused notions about practical subjects. The traditional teaching was in fact, according to the words of the Law, entrusted to the Great Tribunal, as we have already stated in our works on the Talmud. (Introd. to Mishneh Torah and Introd. to Commen. on the Mishnah).
According to the logic of the Rambam, this would also be good reasons for conforming to the second principle of not saying that which has been written. That which is set and fixed and written down should not be taught orally.
However, in our day, due to the diminution of intellect, it has been permitted to learn both orally and by writing. This is due to the principle of “When it is time to do for God, it is permitted to nullify His Torah” In other words, because of the diminution of intellect [in our times] there was a concern that all of Torah would be forgotten [and therefore writing down the oral law became permitted.] This is the conclusion of the Gemora Temurah 14b.
You should also be aware that we find in the Talmud and the Braitot a variety of Rabbinic teachings that seem to take the words of the chumash out of their normal, simple understanding. For example in the Gemora Brachos 32a it says as follows:
What is ‘ And Di-Zahab’? They said in the school of R. Jannai: Thus spoke Moses before the Holy One, blessed be He: Sovereign of the Universe, the silver and gold [zahab] which Thou didst shower on Israel until they said, Enough [dai], that it was which led to their making the Calf. 
In all of these examples [see footnote below], our Sages’ intent is not, God forbid, to actually say that these explanations are the express meaning of the words. Rather, because of the principle of not writing down the oral teachings, it was difficult for students to remember all the oral teachings and even more difficult to remember aggadic teachings. Therefore, our Sages had the idea to pin/attach to a scriptural verse all the sayings that they had been taught in order to make them easier to remember. This works because it is human nature to remember something better if it has a tangible sign that can be seen and felt [like a posuk in the Torah].
Further, we also find that even for laws that were “halacha Moshe m’Sinai” [biblical laws that Moshe received on Mt. Sinai], our Sages also endeavored to find attachments in the text of the Chumash itself. For example, the measurements of separations and partitions mentioned in Eruvin 4b and the details of the knot the tefillin mentioned in Berakot 7a and the issue of pouring of the water libation on Succos mentioned in Rosh Hashana 7a, and many similar examples.
Regarding all of these we find in many places in the Talmud that our Sages praise this ability to find attachments, links and signs [in the text of the Chumash.] As it says in Gemora Shabbos 104a “devise mnemonics in the Torah and thus acquire [memorize] it.” Additionally it says in Gemora Erubin 21a “Besides that Kehelet [King Solomon] was wise, he also taught the people knowledge through affixing signs.” Rashi explains that he established signs whether with the letters of the text [of the Chumash] or with the text of the Mishnah. See also Erubin 54a regarding making signs. In the Yerushalmi Shabbos Chapter 19, Halacha 1, it says, “All Torah that doesn’t have a ‘beit av’ isn’t real Torah.” The commentaries there explain that this means it doesn’t have an example from another place to help one grasp and learn it. Because without this, it will end up being forgotten. This is precisely what we find in many places [in the Talmud] where the Sages attached laws or various conclusions onto the words of some posuk or single word that is only tangentially or even totally unrelated to the topic that is being discussed. For examples, see Shabbos 90b and Ketubot 72b, and Baba Metizah 86a and Baba Metziah 106a and Avodah Zara 8a and Avoda Zara 9a and b and 29a and Chullin 47b and Niddah 45b. The intent in all of these is to make these matters easy to remember as I said above. In this method did they also explain the posuk regarding the butler who “did not remember Yosef and forgot him” which seems redundant. The commentaries explain that the butler did not make a zecher [both remembrance and sign] in order to remember and that precisely therefore he forgot. This similarly is the explanation for the verse “remember what Amalek did to you” which I will explain in its place, God willing. Further, Tosafot write at the end of Gemora Megilla 32a that they were accustomed to learn Mishnayot to a tune since they were learning it orally. With the tune they were able to remember it better. Examine that Tosafot. We already mentioned and we will mention again God willing this general topic with further explanations in various places in our book. For now, we’ve said enough here.
Editor’s Note: This note is simply amazing. His incredible knowledge of the Talmud (Babylonian and Jerusalem) as well his humanity shine through and the way he addresses the reader of his book expresses both.
Further, I think that the Torah Temimah spends so much effort in this note and throughout his book on this topic because he feels this is a very important issue. He is bringing many proofs to show that the rabbis are not explaining these posukim as much as leveraging them as a method to remember received rabbinic and even biblical laws that were taught as “halacha Moshe m’Sinai”. These explanations must not be taken as the pshat or actual meaning of the text.