| Sotah
One of most bitter and divisive (Jewish) fights of the 19th century was that regarding the use of the vernacular in the synagogue - whether in prayer or even in speech. To say the opposition to such was vehement would be an understatement. Add in the fact that the notion of a rabbinic sermon in the vernacular was copied from the Protestant service and we one can begin to understand the bans and calls for excommunication. 

Like most fights that rock the Jewish community the debate went well beyond the halachic issues - people just don’t get as worked up about technicalities themselves - involving hashkafa, one’s worldview, not to mention custom, public policy and fear of the slippery slope. It is precisely those issues where the halacha is either unclear or can be interpreted to allow the issue under discussion, where debates are the fiercest[1]. These same debates, thankfully with much less vehemence, play out in the day school movement where debates over ivrit bivrit are ongoing[2]
The issue of language is discussed most calmly in the Talmud as we transition away from the sotah to a discussion of a wide ranging array of mitzvoth such as prayer, kriat shema, eglah arfuah, birkat hamazon, bikuirm, birkat kohanim, chalitzah. What they all have in common - and in common with the sotah - is that they all involve speech. The Mishna (Sotah 32a) begins by teaching that the kohen’s discussion with the sotah may take place in any language - which likely meant Aramaic. And with that the discussion of the sotah basically comes to an end with some forty percent of the masechet still before us. That forty percent takes as its starting point the ruling of the Mishna as to whether particular mitzvoth may be said in any language or must be said in Hebrew. 
We learn that kriat shema the acceptance of the “yoke of heaven” may be done in any language. This makes eminent sense - language should not be a barrier to devotion to G-d. 
This idea continues in the ruling that prayer cannot be limited to any particular language. Whereas the Gemara seeks scriptural support to determine the language for all of the other mitzvoth, regarding prayer the Gemara simply states that “prayer is mercy, in all ways one may pray” (Sotah 33a). Prayer allows us to beseech, to communicate and meditate with G-d in all languages at all time - “if only man would pray all day” (Brachot 21a) - and in all places. It is the universal language of man.
Similarly one can offer blessings in any and all languages and thus birkat hamazon, blessing and thanking G-d after we eat may be said in any language[3].
Yet if blessings can be said in any language we must explain why the Mishna rules that birkat kohanim, the priestly blessings recited daily, birkat kohen gadol, the special Yom Kippur blessing of the kohen gadol recited in Temple times and birkat hamelech, the blessings of the king during the hakhel  ceremony must be said in Hebrew. Should they too not be allowed to be spoken in any language? 
The mitzvoth that can be recited in any language are those mitzvoth that relate to our personal growth and our personal connection to G-d. The shematefillah, birkat hamazon, the recital of the sotah and personal oaths all focus on the individual. Personal growth requires complete understanding.
National events and symbols require the national language. And the nation of Israel speaks only one language. It is a holy language for a holy people in a holy land. The gathering together of the people to hear the King read the Torah, the daily and yearly blessings of our spiritual leaders must be said in our “official language”. No nation can allow its political and spiritual leaders to speak in any other but the official language. The first chapter of Masechet Yoma describes the tragic scene towards the end of the second Temple period where the high priests could not understand Hebrew. “Zecharia ben Kevutal said: many times I read before him the book of Daniel” (Yoma 18b) as the high priest could not understand the biblical books written in Hebrew.
Similarly the bikurim[4], celebrating the settling of the landand the blessings and curses spoken as the Jews were set to enter the land were to be recited only in Hebrew, reflecting their national character[5].  
[1] This would include the fierce polemic of having a non-Jew play an organ on Shabbat something which abstractly is not difficult to make a case permitting such (and was in fact permitted in Italy until the 1960’s). Fascinatingly the fight over the mechitza was much fiercer than that of the decision of the Conservative movement to allow driving to shul on Shabbat. The prohibition regarding the latter is pretty clear as opposed to the former which has no mention in the classic codes of Jewish law.
[2] Though it seems that the English speakers have save for a few holdouts captured the day. Hebrew is no longer stressed as in years past and more and more schools teach limudei kodesh in English.
[3] Interestingly there is no rabbinic censure of those whose Hebrew is so poor that they must rely on translation to say shemadaven and bench. Let the mitzvoth be done any which way. Yet such censure is given in the case of kiddush. The Mishna is, somewhat surprisingly, silent on whether kiddush need be recited in Hebrew (it need not) yet the Gemara is critical of those men whose Hebrew is so poor that they need to rely on their wife’s recitation of kiddush. Perhaps this is because kiddush may be of lesser importance and hence there is more willingness to be critical when the stakes are not quite as high. Or perhaps ignorance is acceptable if it is pervasive but there is little excuse for a wife but not a husband (or vice versa) to be able to read.
[4] Yet this same parshat bikkurim can (and if need be must) be read in any language when read at the Pesach seder. When educating our children we must make sure they understand clearly. In different contexts, the same exact words can have different meanings and goals. 
[5] Most interestingly it is specifically public prayer that may be said in any language.