Who says that fire cannot become Tamei? If you say that it has no physical material (Mamashus) to be Mekabel Tum'ah (as Rebbi answers), then how can the Gemara make a Kal v'Chomer from fite to Divrei Torah? Divrei Torah do have Mamashus. Even though this Gemara is allegorical, I still do not understand the Kal v'Chomer. (Translation)
Kodem kol, ein zeh kal v'chomer ela hekesh, sh'hukshu divrei Torah l'Esh. V'Shenit, k'mo sh'esh ein bo Mamash (Beitzah 39a), kach Divrei Torah, d'hayinu ha'teivot sh'yotzot m'ha'sefatayim shel ha'adam (k'mevu'ar b'sugya sham), ein bahem mamashus v'einam nifga'im al yiday tum'ato.
V'Da, d'yesh Esh sh'yesh bo mamash, v'hu Esh ha'Ma'arachah (Yoma 21b). Mikol Makom, mistaver sh'af hu eino mekabel Tum'ah, she'harei lo matzanu Tum'ah ela b'chomrim mesuyamim sh'pirtah ha'Torah, v'chol sh'lo ne'emar bo l'hedya kabalat Tum'ah, pashut sh'eino Metamei. (v'Aderaba, Esh metaher k'mo mayim, k'mevuar b'Sanhedrin 39a.)
First, the Gemara is not teaching a Kal v'Chomer, but rather a Hekesh -- Divrei Torah are compared by proximity in the verse to fire. Second, just like fire has no Mamashus (as the Gemara discusses in Beitzah 39a), so, too, Divrei Torah have no Mamashus. This means that the words of Torah that come from one's mouth have no physical, material tangibility (as the Gemara there in Beitzah explains). Thus, they have no Mamashus and cannot be affected by Tum'ah.
Furthermore, it is worth noting that there is a type of fire that does have Mamashus. That is the Esh ha'Ma'arachah (as the Gemara says in Yoma 21b). Nevertheless, it seems that even that fire is not Mekavel Tum'ah, since we only find that Tum'ah affects specific types of materials as specified by the Torah. Any material for which the Torah does not say that it is Mekabel Tum'ah, is not Mekabel Tum'ah. (On the contrary, fire is Metaher from Tum'ah, like water, as the Gemara says in Sanhedrin 39a.)]
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