​ Why can't we eat rice on Passover?

(טו) שִׁבְעַ֤ת יָמִים֙ מַצּ֣וֹת תֹּאכֵ֔לוּ אַ֚ךְ בַּיּ֣וֹם הָרִאשׁ֔וֹן תַּשְׁבִּ֥יתוּ שְּׂאֹ֖ר מִבָּתֵּיכֶ֑ם כִּ֣י ׀ כָּל־אֹכֵ֣ל חָמֵ֗ץ וְנִכְרְתָ֞ה הַנֶּ֤פֶשׁ הַהִוא֙ מִיִּשְׂרָאֵ֔ל מִיּ֥וֹם הָרִאשֹׁ֖ן עַד־י֥וֹם הַשְּׁבִעִֽי׃

(15) Seven days you shall eat unleavened bread; on the very first day you shall remove leaven from your houses, for whoever eats leavened bread from the first day to the seventh day, that person shall be cut off from Israel.

(ה) אלו דברים שאדם יוצא בהן ידי חובתו בפסח: בחטים, בשעורים, בכסמין ובשיפון ובשבלת שועל.

(5) These are the [grains] with which a person may discharge his [obligation to eat matzah] on Passover: with wheat, with barley, with spelt, and with rye, and with oats.

אמר רב אשי שמע מינה דרב הונא לית דחייש להא דרבי יוחנן בן נורי דתניא רבי יוחנן בן נורי אומר אורז מין דגן הוא וחייבין על חימוצו כרת ואדם יוצא בו ידי חובתו בפסח.

Rav Ashi said: From Rav Huna you may infer that none pay heed to the following [ruling] of Rabbi Yochanan ben Nuri. For it was taught, Rabbi Yochanan ben Nuri said: "Rice is a species of grain and [a person shall be] cut off for [eating it in] its leavened state, and a person may discharge his [obligation to eat matzah] with it on Passover."

ספר מצוות קטן, הגהות רבינו פרץ מצוה רכב:

ועל הקטניות כגון פוה'"ש ופול"י ורי"ש ועדשים וכיוצא בהם רבותינו נוהגים בהם איסור שלא לאוכלם בפסח כלל ... דבר שנוהגין בו העולם איסור מימי חכמים הקדמונים.

Sefer Mitzvot Katan, Glosses of Rabbi Peretz of Corbeil (France, 13th Century), Mitzvah 222

Legumes such as fava, beans, rice, and lentils and the like, our teachers have the custom of a prohibition not to eat them during Passover at all ... a prohibition that was a custom of the world from the days of the ancient sages.

רבינו ירוחם - תולדות אדם וחוה נתיב ה חלק ג דף מא טור א:

ואותם שנהגו שלא לאכול אורז ומיני קטנית מבושל בפסח מנהג שטות הוא זולתי אם הם עושין להחמיר על עצמן ולא ידעתי למה.

Rabbenu Yerucham (Provence, 14th Century) - Toldot Adam VeChava, Path 5, Section 3, Page 101, Column 1

Those who are accustomed to not eat cooked rice and beans on Passover, this is a foolish custom, unless they do so to be stringent, and I do not know why.

Eating Kitniyot (Legumes) on Pesach (English Summary)

Rabbi David Golinkin - responsafortoday.com/engsums/3_4.htm

Hebrew teshuvah - responsafortoday.com/vol3/4.pdf

Article in Voices of Conservative/Masorti Judaism - cjvoices.org/article/the-kitniyot-dilemma

[T]here are many good reasons to do away with this "foolish custom": a) It detracts from the joy of the holiday by limiting the number of permitted foods; b) It causes exorbitant price rises, which result in "major financial loss" and, as is well known, "the Torah takes pity on the people of Israel's money"; c) It emphasizes the insignificant (legumes) and ignores the significant (hametz, which is forbidden from the five kinds of grain); d) It causes people to scoff at the commandments in general and at the prohibition of hametz in particular - if this custom has no purpose and is observed, then there is no reason to observe other commandments; e) Finally, it causes unnecessary divisions between Israel's different ethnic groups. On the other hand, there is only one reason to observe this custom: the desire to preserve an old custom. Obviously, this desire does not override all that was mentioned above. Therefore, both Ashkenazim and Sephardim are permitted to eat legumes and rice on Pesah without fear of transgressing any prohibition.