Why do we do Chazaras HaShatz for Shacharit and Mincha, but not for Maariv?
(It would be appreciated if you can find a source/support)
Rabbi Kaganoff points out that Rav Yosi ben Chanina in the Gemor makes the statement that each of the Avos instituted one daily prayer with Yaakov in Vayeitzei being shown to have instituted Ma'ariv. The question that arises is how Ma'ariv can be a reshus when Yaakov Avinu caused it to become requires (like Avraham and Yitzchak with Shacharis and Mincha). Yaakov was "forced" into Ma'ariv when the sun set unexpectedly in Parsha Vayeitzei), so it is not the same level of requirement.
However, Rabbi Yehoshua ben Levi connects the three to the daily services with Shacharis and Mincha being the daily tamid, while Maariv is the burning of the limbs that are "remaining" (Brachos 26b)
As a result, while davening Maariv is required, it is a lesser degree of requirement, since there were not always sufficient karbanos to require burning at night.
He also brings up the incident of Rabban Gamliel and Rabbi Yhoshua in which Rabban Gamliel which led to Rabban Gamliel's (temporary) removal and the appointment of Rabbi Eliezer ben Azaria.
Is maariv optional? Ultimately, the halachic conclusion is that maariv is a reshus. Is maariv really optional? Can one decide, every night, if he wants to skip maariv?
The rishonim already note a ruling that appears to contravene the statement that maariv is optional. Someone who missed maariv must recite a makeup prayer, called a tefillas tashlumim, after the next morning's shacharis. However, this ruling appears to contradict the statement that tefillas arvis reshus. If maariv is optional, why must someone make up the missed prayer?
In response to this question, Tosafos explains that when the Gemara states that maariv is reshus, it does not mean that it is optional, but that it is less obligatory than other requirements. For example, should one need to choose between fulfilling two different mitzvos in a situation where one cannot fulfill both of them, maariv is pushed aside (Tosafos, Brachos 26a s.v. Ta'ah). In all other circumstances, one is obligated to recite maariv. The Rif answers the question in a different way. He explains that, indeed, maariv is technically not obligatory. However, someone who decided to recite maariv this evening makes it obligatory on himself and must pray correctly, even if he needs to pray a makeup.
According to the interpretation that the forefathers instituted the daily prayers, although Yaakov was the first to daven maariv, he had not intended to daven so late, but Hashem caused the sun to set suddenly, giving Yaakov no choice but to daven after nightfall. Since this davening was performed not as Yaakov's first choice, but because he had no other option, the prayer instituted this way is reshus (Pnei Yehoshua, Brachos 26b s.v. Mihu).
According to the approach that our prayers correspond to the daily offerings, shacharis and mincha each represent the daily korban tamid that was offered in the Beis Hamikdash. Maariv represents the remaining parts of the daily tamid that were burnt the following night on the mizbei'ach. Since this step in the processing of the korban is non-essential, the prayer was also not required (Rashi, Shabbos 9b, s.v. Lemaan).
Why does maariv not include a chazzan's repetition of shmoneh esrei, whereas there is one for both shacharis and mincha? The answer is that although today maariv is obligatory, it is not the same level of requirement as are shacharis and mincha. Since everyone is required to daven shacharis and mincha, Chazal were concerned that unlettered individuals would be unable to fulfill the mitzvah. Chazal therefore instituted the repetition of the tefillah, so that those unable to daven otherwise would be able to fulfill their requirement by listening to the chazzan's prayer. However, since maariv is reshus, Chazal were less concerned that the unlettered would be unable to fulfill this responsibility, and therefore, they did not institute a repetition.