The Haggadah quotes the famous Mishnah in Maseches Berachos (דף י"ב:) which cites the statement of Rabbi Elazar Ben Azaryah who said that although he was some seventy years of age, he was unable to prove that one should make reference to Yetzias Mitzrayim at night as well as during the day. Ben Zoma, however, succeeded in explaining it by referring to the Posuk (דברים ט"ז:ג) which obligates each Jew to recall Yetzias Mitzrayim "כל ימי חייך," "all the days of your life." Had it said "ימי חייך," the days of your life, the obligation would've been only during the daytime. But since it says "כל ימי חייך," all the days of your life, night-time is included in this obligation as well.
Earlier in the same section, the Torah states "כי בחדש האביב הוציאך ה' אלקיך ממצרים לילה," teaching that Hashem took Bnai Yisrael out of Mitzrayim at night (שם פסוק א). Apparently, even though we know that Hashem really took Bnai Yisrael out during the day, the redemption itself had already taken place, or at least started, on the preceding night. Why then should it be necessary to provide a special proof from the Torah for the requirement to make mention of Yetzias Mitzrayim at night as well? The necessity for providing such a proof regarding the night (when none is necessary regarding the day) implies that the Mitzvah of mentioning Yetzias Mitzrayim actually applies primarily to the daytime. This implication may offer us some valuable insight into the significance of this Mitzvah, as explained by Rav Shimshon Raphael Hirsch.
Both the passive and the active aspects of our lives, our destiny and our deeds, have their basis in Yetzias Mitzrayim. From that event, we derive our trust in Hashem regarding our fate, and the awareness of our obligation to Him regarding our deeds. Our trust in Hashem and His direction of our fate expresses itself mainly during the dark periods, or the "nights," of our lives. On the other hand, the submission of our actions to His discipline must be proven during the working hours of the day.
At first glance, one might be led to the conclusion that from the story of Yetzias Mitzrayim, we are to learn mainly that we must have trust in Hashem's Providence, and thus should apply the commandment of remembering the events of Yetzias Mitzrayim primarily during the night. Jewish thinking, however, realizes that it is easier to trust Hashem during the "darkness" of our lives than it is to remain faithful to our obligations in the bright sunlight of our daily lives. It therefore follows that the constant renewal of our awareness of our duties as Jews is actually much more important, and that the primary emphasis of the recitation of Kerias Shema must consequently be during the day. Rabbi Elazar Ben Azaryah therefore had no doubt about this point. He was simply looking for an allusion in the text to make this commandment applicable to the night-time as well. He found it in the additional word "כל," all, indicating that although awareness of Hashem may indeed be more obvious and easier during the night, there is still an obligation to make specific mention of it by recalling Yetzias Mitzrayim at night too.