Three possible reasons are offered for the Torah’s prohibition of making an altar with cut stones (Ex. 20:25). You may only use stones that have not been shaped by iron. Noting that the Torah used the word for sword, Rashi and Ramban (ad loc.) follow the Sages (Mekhilta, ad loc.) in explaining that metal, and swords in particular, are used to shorten life while the altar is designated to extend life.
Rambam (Moreh Nevukhim 3:45) says that the above is nice homiletics but the real reason for this prohibition is to avoid an idolatrous practice. Ancient idolaters would smooth their altars with metal and therefore the Torah forbade Jews from doing the same. Our religious practices may not imitate foreign practices. “The object of all these commandments is the same, namely, that we shall not employ in the worship of God anything which the heathen employed in the worship of their idols” (Friedlander tr.).
Ramban (ibid.) challenges the Rambam’s view with the following: Halakhah only forbids shaping the stones with iron; silver is fine. However, the end result would look the same, just like the idolaters’ altars.
Perhaps a greater challenge comes from history. Victor Hamilton (Exodus: An Exegetical Commentary, p. 365) argues that “Archaeologists have found Canaanite altars made of such [uncut] stone, so that would rule out any anti-Canaanite polemic.” Rashbam (ad loc.) offers a similar explanation that bypasses the historical question. He suggests that the artisans carving an altar may incorporate a statue into it. Shadal (ad loc.) agrees.
However, a 1968 doctoral dissertation on just the three verses Exodus 20:24-26 (Diethelm Conrad, Studien zum Altargesetz, Warburg) argues that the Rambam treads on solid historical ground. I do not have access to the dissertation and would not understand it even if I did. The secondary literature I have seen offers two versions of
Brevard Childs (Book of Exodus, p. 466) writes that Conrad argues “specifically directed against the adopting of Canaanite altars which were made of finished stone.” However, Joe Sprinkle (The Book of the Covenant: A Literary Approach, p. 48 n. 2) says that Conrad sees the prohibition as “forbidding ostentation by means of a particular treatment of the altar involving the chiselling out of so-called bowl-holes for libations in the Canaanite pattern known from archaeology.” Either way, Conrad seems to reach a conclusion similar to Rambam’s, validating its historical possibility.
Abarbanel (ad loc.) quotes an entirely different approach from Ibn Kaspi. An object’s natural form is more proper than an artificial form. One word for shaping is posel, as Moshe’s writing on the tablets is called (Ex. 34:4). This word also means to invalidate. Removing something from its natural form is, in some sense, lowering its status. The altar should be made from stones in their highest form–natural. This idea sounds strange to me. Certainly cut and polished diamonds are considered higher than when in their natural state. Gold and silver are also more highly valued when polished and shaped.