“And you shall teach them to your children, to speak in them when you sit in your house, when you walk by the way, when you lie down, and when you rise up.” (Devarim 11:19)
Rashi on the words “to speak in them” quotes the Sifrei that when a child first begins to talk, his parents should speak to him in Hebrew and teach him Torah, and this will guarantee the child a long life. This same idea is found in the Tosefta in Chagigah which states that when a child knows how to talk, his parents should teach him Hebrew.
The clearest source which identifies learning Hebrew as a mitzvah is found in the Rambam’s commentary on the Mishna in Pirkei Avot, chapter 2. The Mishna states that one must be as careful regarding a minor mitzvah as one is with a major mitzvah. As an example of a minor mitzvah, the Rambam cites studying and speaking Hebrew. The Rambam here clearly considers learning and speaking Hebrew to be a mitzvah, even though people think it is a minor mitzvah.
The difficulty is that although the Rambam’s view is clear in his Mishna commentary, he does not codify this mitzvah of learning or speaking Hebrew in his Mishneh Torah, nor does such a mitzvah appear in the Shulchan Aruch. The Torah Temimah on Parshas Eikev wonders why the poskim omitted any reference to the requirement to learn and speak Hebrew. However, Rabbi Moshe Feinstein in Iggros Moshe, Even Ha’ezer chapter 35, actually states clearly that there is a mitzvah to speak Hebrew, although he notes that there is no prohibition against speaking in any other language.
The Ramban in Parshas Ki Sisa writes that Hebrew is called Lashon Hakodesh precisely because it is the language used by the Holy Torah. The Yerushalmi in Shabbos states that one who speaks Lashon Hakodesh is guaranteed a place in Olam Haba. The Korban Ha’eidah explains this Talmudic passage to mean that speaking Hebrew leads to spiritual purity.
It is interesting to note that the Shulchan Aruch in Orach Chaim (Chapter 307) rules that whereas it is not appropriate to read certain types of literature on Shabbos, if they are written in Hebrew, they may be read on Shabbos. The Magen Avraham explains that this is because the Hebrew language itself has kedushah, and one can learn how to learn Torah simply by reading books and even letters written in Hebrew.
The Midrash in Vayikra Rabba states that even though the Jews were at the 49th level of impurity in Egypt, they were still worthy of redemption because they continued to speak Hebrew. The Midrash brings other reasons why we merited redemption, but we see that speaking Hebrew is your identity card for being a member of the Jewish People.