הַלְּבֵנִים וְהַשַּׁיִשׁ אֵינָן חֲשׁוּבִין כַּאֲבָנִים
Bricks and Marble aren't considered stones.
What is the reason for this decision?
Rambam is based on Nega’im 12:2, which states (based on Vayikra 14:45) that a house needs to be composed of stone, wood and earth in order to contract tzara’at impurity, and that marble does not count.
Tiferet Yisrael in Bo’az 3 explains that marble is never referred to as simply “stone” but instead “stones of marble”.
This is a purely speculative idea. But it's worth considering since you are looking for a "reason" behind the mitzvah and not a discussion of the halacha itself. Why is marble not considered like other stones.
Rambam distinguishes in this halacha between 2 categories, 1) "stones" (אבן) together with soil and wood and 2) "bricks" (לבנים) and "marble" (שיש).
You could postulate that bricks are man-made, which would also agree with the idea that tiles are in the same category as bricks in regard to this halacha. Tiles and bricks are formed by subjecting mud or clay to extreme heat. The heat causes them to take on different qualities in terms of hardness and durability than the original clay.
But marble is generally, naturally occurring.
That takes you to the subject of geology. Rocks & stones fall into 3 general classifications, Igneous, Sedimentary and Metamorphic. The 1st two are essentially derived from the earth's crust and are in their original state.
Igneous rocks originate from lava which cools and crystalizes. They are in their original state of being. Sedimentary rocks are like concrete. Igneous rocks that have worn away through erosion, and other matter that are carried in water mix together, and then precipitate out in sediment. Then over time with moderate temperature and pressure from what lays on higher levels of sediment, the sedimentary rock forms through compaction.
Metamorphic rock, of which marble is included, is also originally a composite but is different in that high pressure and extreme temperature change the physical properties and chemical composition of the resulting stone. It takes on completely new qualities and properties. Although naturally occurring, it is a very similar formation process as that of brick and tile.
And so this transformation process or metamorphosis is what seems to be common in relation to marble, brick and tile. And would suggest that this is why marble is distinguished from other stone.
For those who might be interested in some additional insights into the relationship between these 3 elements of marble, brick and stone, it is brought in the writings of Rabbi Tzadok HaKohen of Lublin that marble (שיש) is associated with the Supernal concept of Gevurah of Ain Sof which he says is responsible for the Tzimtzum HaRishon (צמצום הראשון) which made possible the entire creation.
In kabbalistic literature, this is the initial transformation from Infinite (אין, אין סוף, בלי גבול) to Finite (יש, גבול) which resulted in what is called the Makom Panuy (מקום פנוי, החלל), meaning a place or possibility that appeared devoid of G-d. This is often referred to as Creation Yesh mi'Ayin (יש מאין) or Creation Ex-Nihilo. It is like a quantum leap (דילוג) from one state to a completely different state.
Rabbi Moshe Zacuto in his introduction to Sefer Mevo Sha'arim, pg. 5, and Rabbi Moshe Chaim Luzzato in Sefer Adir B'Marom, pg. 92 of the Friedlander edition explain that this is associated with the transformation of G-d's name (יה-יה) via A't-Ba'sh. That the name becomes (צם-צם) Tzam-tzem.
If the same A't-Ba'sh transformation is applied to bricks (לבנים), the item associated with marble, the result is (כשטמ׳י) which has a gematria value of 379. This is also the value for the G-d of material existence (אל הגשם) which alludes to the teaching from Rabbi Tzadok, the Ramaz and the Ramchal mentioned above.
If stone (אבן), that category which is distinct from marble and bricks, is considered in similar fashion it is noted that the gematria is 53, which is also דילוג (the quantum leap mentioned above) and הגדולה, which is the kabbalistic term associated with Chesed of Ain Sof, the polar opposite of that which manifested the Tzimtzum HaRishon, Gevurah of Ain Sof like is mentioned above.
And if the A't-Ba'sh transformation is applied to אבן, the resulting gematria is 709 which happens to be אין מזל לישראל, the expression of the Sages that indicates Israel is not under the direction or supervision of G-d's Heavenly-Angelic system from creation, but rather from G-d directly (Hashgacha Pratit) Divine Providence.
And to associate all this with the time we currently face, Erev Tisha b'Av 5780, (709 תש׳ט), the A't-Ba'sh of אבן, is also the gematria of יעקב יצחק הורוביץ, the Seer of Lublin (החוזה מלובלין) whose 205th Yartzeit falls on the 9th of Av.
In his memory and merit and in keeping with the concepts mentioned above contrasting and comparing stone, marble and bricks and how G-d can immediately transform any situation even in the blink of an eye, may we all see the transformation of all sadness to joy, all bitterness to sweetness and all darkness to light, immediately and without delay.