Power Of Speech
במדרש זכור את א"ע ה"א למרים משל למטרונא כו' כך מרים אמרה שירה כו' ע"ש הענין הוא להיות כח איש ישראל בפה לכן צריכין לשמור הפה מלה"ר
In the Midrash on "Remember what Hashem your God did to Miriam" (Devarim 24:9): a parable to a noblewoman, and so forth — so too Miriam sang the shirah, and so on (see there). The matter is that the strength of a Yid lies in the mouth, and therefore one must guard the mouth from lashon hara.
The Midrash on the command to remember what happened to Miriam teaches that a Yid's essential power is the power of speech, which is why one must so carefully guard his mouth against lashon hara.
ומרים הי' בחי' תורה שבע"פ לכן באר בזכות מרים שהיא פי הבאר דכ' עלי באר ענו לה שהיא בחי' תורה שבע"פ וע"ש זה נק' מרים פועה שפועה אל הילד ע"ש
Miriam embodied the aspect of Torah she'baal peh, the Oral Torah, and therefore the well came in Miriam's merit, for she is the mouth of the well, as it is written, "Rise up, O well — sing out to it" (Bamidbar 21:17), since she is the aspect of Torah she'baal peh; and on account of this she is called "Miriam Puah," for she would coo to the child, as is explained there.
Miriam corresponds to the Oral Torah — the spoken Torah — and so the miraculous well was given in her merit, she being its 'mouth,' and her name Puah reflects this power of the mouth in soothing a child.
ולפי שהי' כחה גדול בפה נתענשה בדברה על משה כמ"ש שמדקדק עם הצדיקים כחוט השערה:
And precisely because her strength in the mouth was so great, she was punished when she spoke about Moshe Rabbeinu, as it is written that the Holy One, Blessed is He, is exacting with the tzaddikim to a hairsbreadth.
Because Miriam's greatness was specifically in her power of speech, that very faculty was where she was held accountable when she spoke against Moshe Rabbeinu, since Hashem measures tzaddikim with exacting precision.
Summary: The Sfas Emes explains that the essential strength of a Yid resides in the mouth — the power of speech — which is why the Torah demands such vigilance in guarding the mouth from lashon hara. Miriam personified this power, for she embodied Torah she'baal peh, the Oral Torah; it was therefore in her merit that the well sustained Bnei Yisrael, she being its very 'mouth,' and even her name Puah reflects this faculty of speech. Yet precisely because her strength lay in the mouth, that was where she was held to account when she spoke about Moshe Rabbeinu. This reflects the principle that the Holy One, Blessed is He, is exacting with tzaddikim to a hairsbreadth, demanding the most from one's greatest strength.