(רמ״א) הגה: ונוהגים להניח פתיתי חמץ במקום שימצאם הבודק כדי שלא יהא ברכתו לבטלה (מהר"י ברי"ן).
Rama: We have a custom to put out small pieces of Chametz, so that the person searching will find them, so that his blessing will not be in vain.
This seems to be a Chumra and a stringency that follows the din of getting rid of Chametz, and other poskim try to figure out the nature of why having Chametz around on Pesach is so much more strict than other forbidden foods in Halacha.
The Radvaz then makes one last comparison. He says that there is a special mitzvah to seek out and destroy all Avoda Zara or any type of idolatry that one might find among us. However, that mitzvah only applies in Eretz Yisrael! We don't have the mitzvah to search and destroy Avoda Zara outside of Israel, instead, if we happen to conquer a place, only then are we commanded to destroy the Avoda Zara that's there.
The Radvaz says, I DON'T GET IT! How is it possible that Chametz is stricter than Avoda Zara?!
He finally reaches the conclusion that there can only be one explanation for how that can be. He says the following.
מ"מ הרי אתה רואה שלא החמירה תורה בעכו"ם כמו בחמץ הילכך עדיין צריך טעם ועל כן אני סומך על מה שאמרו רז"ל במדרשות כי חמץ בפסח רמז ליצה"ר והוא שאור שבעיסה ולכן כלה גרש יגרש אותו האדם מעליו ויחפש עליו בכל מחבואות מחשבותיו ואפילו כל שהוא לא בטיל.
In any case, you see here that the Torah was not as stringent with idolatry like it is with Chametz. Therefore, we still need a reason, and I rely on our rabbis, of blessed memory, in the Midrash that says that Chametz is an allusion to the evil inclination, and that is [also like] yeast in the dough [that will make it rise with even a little bit], and thus a person should banish it from himself, and search for it in all of the hidden areas of his thoughts, and even a slight trace is not nullified.
(ב) כְּתִיב (שמות לה) אֱלקֵי מַסֵּכָה לא תַעֲשֶׂה לָּךְ, וּכְתִיב בַּתְרֵיהּ אֶת חַג הַמַּצוֹת תִּשְׁמֹר. (מאי עביד) מַאי הַאי לְגַבֵּי הַאי. אֶלָּא הָכִי אוּקְמוּהָ, מַאן דְּאָכִיל חָמֵץ בְּפֶסַח (כאילו עביד כוכבים ומזלות למפלח לגרמיה, דהא רזא הכי הוא דחמץ בפסח) כְּמַאן דְּפָלַח לְכּוֹכָבִים וּמַזָּלוֹת אִיהוּ.
(2) It's written ״You shall not make molten gods for yourselves” (Shemot 34:17) and afterwards it is written ״You shall keep the feast of unleavened bread (Ibid 34:18).” What does this [verse] have to do with that one? Rather, this is the explanation: one who eats chametz on Pesach is similar to one who worships idols.
והתניא ר"ש בן אלעזר אומר משום חילפא בר אגרא שאמר משום ר' יוחנן בן נורי המקרע בגדיו בחמתו והמשבר כליו בחמתו והמפזר מעותיו בחמתו יהא בעיניך כעובד ע"ז שכך אומנתו של יצה"ר היום אומר לו עשה כך ולמחר אומר לו עשה כך עד שאומר לו עבוד ע"ז והולך ועובד א"ר אבין מאי קראה (תהלים פא, י) לא יהיה בך אל זר ולא תשתחוה לאל נכר איזהו אל זר שיש בגופו של אדם הוי אומר זה יצר הרע
Anger
Wasn’t it taught in a baraita that Rabbi Shimon ben Elazar says in the name of Ḥilfa bar Agra, who said in the name of Rabbi Yoḥanan ben Nuri: One who rends his garments in his anger, or who breaks his vessels in his anger, or who scatters his money in his anger, should be like an idol worshipper in your eyes, as that is the craft of the evil inclination. Today it tells him do this, and tomorrow it tells him do that, until eventually, when he no longer controls himself, it tells him worship idols and he goes and worships idols. Rabbi Avin said: What verse alludes to this? “There shall not be a strange god within you, and you shall not bow to a foreign god” (Psalms 81:10). What is the strange god that is within a person’s body? Say that it is the evil inclination. One may not rend his garments in anger, because in doing so he is deriving pleasure from satisfying the evil inclination.
Falsehood
And Rabbi Elazar says: With regard to anyone who amends the truth in his speech, it is as though he worships idols. As, it is written here, in the verse where Jacob sought to resist taking his father’s blessing from Esau: “And I shall seem to him a deceiver [metate’a]” (Genesis 27:12), and it is written there with regard to idol worship: “They are vanity, the work of deception [tatuim]” (Jeremiah 10:15).
א"ר יוחנן משום ר"ש בן יוחי כל אדם שיש בו גסות הרוח כאילו עובד עבודת כוכבים כתי' הכא (משלי טז, ה) תועבת ה' כל גבה לב וכתיב התם (דברים ז, כו) ולא תביא תועבה אל ביתך
Arrogance
Rabbi Yoḥanan says in the name of Rabbi Shimon ben Yoḥai: Any person who has arrogance within him is considered as if he were an idol worshipper, as it is written here: “Everyone that is proud in heart is an abomination to the Lord” (Proverbs 16:5), and it is written there concerning the destruction of idols: “And you shall not bring an abomination into your house” (Deuteronomy 7:26).
Rav Asher Weiss explains that when Bnei Yisrael were given the Mitzvah to do the Korban Pesach, they were first told to draw out their hands, "משכו", before actually taking the lamb for the Korban Pesach. The Midrash Rabbah explains that the extra word of "משכו" is referring to Avoda Zara, that they should remove their hands from serving idolatry before doing the mitzvah of the Korban Pesach. Only then, could they do the Korban, which was the key to them leaving Egypt.
(כא) וַיִּקְרָ֥א מֹשֶׁ֛ה לְכָל־זִקְנֵ֥י יִשְׂרָאֵ֖ל וַיֹּ֣אמֶר אֲלֵקֶ֑ם מִֽשְׁכ֗וּ וּקְח֨וּ לָכֶ֥ם צֹ֛אן לְמִשְׁפְּחֹתֵיכֶ֖ם וְשַׁחֲט֥וּ הַפָּֽסַח׃
(21) Moses then summoned all the elders of Israel and said to them, “Go, draw out lambs for your families, and slaughter the passover offering.
מִשְׁכוּ וּקְחוּ לָכֶם, כְּלוֹמַר מִשְׁכוּ יְדֵיכֶם מֵעֲבוֹדַת כּוֹכָבִים, וּקְחוּ לָכֶם צֹאן, וְשַׁחֲטוּ אֱלֹהֵיהֶם שֶׁל מִצְרַיִם וַעֲשׂוּ הַפֶּסַח, שֶׁבְּכָךְ הַקָּדוֹשׁ בָּרוּךְ הוּא פּוֹסֵחַ עֲלֵיכֶם.
"Draw out"- that is to say, draw out- your hands from idolatry, and "take for yourselves sheep"- slaughter the gods of the Egyptians and make the Korban Pesach, for it is because of that, the Holy One, Blessed is He, passes over you ("Pesach").
Despite their faults, Hashem displayed his love and mercy for his children and believed in them. So too, the holiday of Pesach represents a similar idea for us, their descendents celebrating Pesach today, that we should use this opportunity to rise above our faults, and draw close to Hashem.
The Baer Heitev in the Shulchan Aruch quotes the Arizal as saying a pretty bold statement.
(א) האר''י ז''ל כתב הנזהר ממשהו חמץ בפסח מובטח לו שלא יחטא כל השנה:
The AR"I Z"L wrote that one who is careful to avoid any trace of Chametz, is guaranteed to not sin the entire year.
Rav Asher Weiss in the Minchas Asher suggests that maybe we do it to remind ourselves of a sad but true fact, that although we blame the Yetzer Hara for our sinning, we are largely responsible for our own faults. He says, "with our own hands, we plant the seeds of darkness that sprout in our hearts. When we wantonly pursue our selfish pleasures or give free rein to our anger, we nurture the negative character traits, the 'Chametz of the heart', which we must later work so hard to destroy."
Only after we spread out the chametz during the bedika, do we remind ourselves how to carefully look for every crumb of Chametz, physically, and spiritually. We should be zoche this year to rid our hearts of the chametz of selfishness, falsehood, and arrogance, and replace them with generosity, kindness, and ahavas Yisrael.