We say in the Haggadah, quoted from the Mechilta:
יָכוֹל מֵראשׁ חֹדֶשׁ? תַּלְמוּד לוֹמַר בַּיּוֹם הַהוּא. אִי בַּיּוֹם הַהוּא יָכוֹל מִבְּעוֹד יוֹם? תַּלְמוּד לוֹמַר בַּעֲבוּר זֶה - בַּעֲבוּר זֶה לֹא אָמַרְתִּי, אֶלָּא בְּשָׁעָה שֶׁיֵּשׁ מַצָּה וּמָרוֹר מֻנָּחִים לְפָנֶיךָ.
It could be from Rosh Chodesh [that one would have to discuss the Exodus. However] we learn [otherwise, since] it is stated, "on that day." If it is [written] "on that day," it could be from while it is still day [before the night of the fifteenth of Nissan. However] we learn [otherwise, since] it is stated, "for the sake of this." I didn't say 'for the sake of this' except [that it be observed] when [this] matsa and maror are resting in front of you [meaning, on the night of the fifteenth].
Why does the Haggadah not pose the option of saying it on the fifteenth? Why is that any less logical than the fourteenth?