Actually, Mädchen (meaning “girl” in German) is a diminutive. It comes from Magd (an old word for “maid” or “young woman”) with the -chen suffix, which is a common diminutive in German.

The -chen suffix makes words grammatically neuter, which is why Mädchen takes das instead of die, even though it refers to a female person.

I’m not German but the same applies to the Dutch word for girl, and we’ve the same rule for neutral. By the way, ‘magd’ in Dutch means virgin (maagd to be precise), which sounds incredibly inappropriate to be going around calling someone; little virgin (/¯ ಠ_ಠ)/¯