The Torah prohibits the “destruction” of one’s beard (Leviticus 19:27). The Rambam explains this prohibition as shunning the ways of idolatry. Indeed, the Yiddish word for priest, goloch, derives from the Hebrew for shaven. The Christian priests’ smooth face was their distinguishing trait.
The Chatam Sofer (1762–1839) rules that there isn’t anything unJewish about shaving one’s beard, as long as you do not “destroy it”. He explains that Jewish men shaved their beards during the Crusades to avoid standing out and since then, Jews have been shaving.
When the two-blade electric razor hit the market (with the outer screen acting as the first blade), Rav Moshe Feinstein (1895–1986) permitted it because he understood the ban as specifically on manual razors, which destroy the hair.
It may seem hair-splitting to forbid shaving with a razor. But, it is a fundamental of halachah that there are some mitzvot that we obey simply because God commanded.