Our Gemara on amud Aleph tells us that while prayers can technically be said in any language, there are metaphysical barriers when the prayer is not in the holy tongue, l’shon kodesh:

תְּפִלָּה רַחֲמֵי הִיא כׇּל הֵיכִי דְּבָעֵי מְצַלֵּי

It is stated in the mishna that the Amida prayer may be recited in any language. The reason for this is that since prayer is a request for divine mercy, one may pray in any way that one desires.

וּתְפִלָּה בְּכׇל לָשׁוֹן וְהָאָמַר רַב יְהוּדָה לְעוֹלָם אַל יִשְׁאַל אָדָם צְרָכָיו בִּלְשׁוֹן אֲרָמִית דְּאָמַר רַבִּי יוֹחָנָן כׇּל הַשּׁוֹאֵל צְרָכָיו בִּלְשׁוֹן אֲרַמִּי אֵין מַלְאֲכֵי הַשָּׁרֵת נִזְקָקִין לוֹ לְפִי שֶׁאֵין מַלְאֲכֵי הַשָּׁרֵת מַכִּירִין בִּלְשׁוֹן אֲרַמִּי

The Gemara asks: But may prayer really be recited in any language? But didn’t Rav Yehuda say: A person should never request in the Aramaic language that his needs be met, as Rabbi Yoḥanan said that with regard to anyone who requests in the Aramaic language that his needs be met, the ministering angels do not attend to him, as the ministering angels are not familiar [makkirin] with the Aramaic language?

לָא קַשְׁיָא הָא בְּיָחִיד הָא בְּצִבּוּר

The Gemara answers: This is not difficult, as that statement of Rabbi Yoḥanan is referring to the prayer of an individual, who needs the support of the angels, whereas this statement of the mishna is referring to communal prayer.

Angels who carry the prayers do not recognize Aramaic, and thus in private prayer one should refrain from Aramaic. Tosafos (Shabbos 12b) wonders, how it is possible that angels, “who even know the inner thoughts of a man”, cannot understand Aramaic?

A simple answer to Tosafos’ question is that knowing inner thoughts is not the same as speech. As we discussed extensively in Psychology the Daf Sotah 18, all-encompassing superior knowledge is not the same as knowing a specific temporal outcome. We used the following metaphor:  

Imagine you are an expert computer programmer. Let us say you designed and programmed the ultimate word processor. It can do everything anybody imagines: spellcheck, cut and paste, grammar suggestion, formatting, colorful graphics, and fonts. It has an amazing graphical user interface and is user-friendly. Let us further imagine that you are blind. You’re a brilliant programmer, but you never will use this word processor. You never will experience subjectively what it’s like to benefit from all these features. Yet, at the same time, you know more than any user of the program. You know everything the program can do. The one thing you don’t know, is the subjective experience of using the program. Even though there is no trick, no device, no clever permutation, that you in some way did not foresee because you wrote the program, at the same time, you have no subjective experience of any of those features. 

The expression of human speech is a distillation and moment specific crystallization of various conscious and unconscious thoughts. Just because one can read a person’s thoughts does not mean one will know what the person will say.

What is the reason why angels do not understand Aramaic? There are several Teshuvos of the Ramah (127,127 &130) where he explains, quoting the Kuzari, that Aramaic is a distorted form of Hebrew so the angels cannot recognize a distortion. This is understandable, because it being that works with absolute truth, might not be able to go down to the granular level of a mode of a expression at the moment. (In that way, it is really similar to what we said above.) 

Along these lines, the Shalah (Rosh Hashanah, Ner Mitzvah 47) considers the possibility that the Gemara here means to say that all languages aside from Hebrew are not preferred because all languages are not understood by the angels.  Aramaic was mentioned by the Gemara as an extra chiddush, because since it is close to Hebrew and was used of Onkelos as well as having some words in the Torah as Aramaic, one might think the angels would understand Aramaic. Also see Rav Tzaddok (Dover Tzedaka, Acharei Mos 4). Ha’amek Davar (Devarim 1:45), seems to learn our Gemara in a similar manner, differentiating between heartfelt cries of anguish that require no language, versus formal prayer. (Even this answer can be strengthened conceptually with the point we made earlier. We might take the position that Angels can only understand absolute truths, therefore if it is just a cry of anguish, with nothing articulated, and just an emotion,  the angels can get the truth of that. However, language that uses figures of speech that are later inventions may elude them.)

Akeidas Yitschok (58), who trends to more rationalist philosophical interpretations (Yitschok Arama, a Spanish Rishon who lived through Inquisition), offers a simple explanation of our Gemara. The rabbis wanted to encourage the regular folk to enhance their understanding and use of l’shon kodesh for precision and mental purity in their prayers., and used a superstitious motivator, such as the “angels won’t bring your prayers up.”

While this may seem dishonest, it was the way of Chazal to sometimes frame issues of concern within a superstitious context to intimidate and spook the Amey Ha’aretz into compliance. We discussed this in some depth in Psychology of the Daf, Succah 43, click here https://nefesh.org/SimchaFeuerman/succah--noble-lies-covid-and-the-rabbis-psychology-of-the-daf-/read