I would like to add, that 'Mädchen' is a diminutive. Diminutive means to make somethin like a 'pet name' of any german noun.
Suffixes for diminutives are "chen" or "lein".
Any german noun could be prolonged with 'chen' or 'lein' and changes grammatically automaticly to neutrum.
Der Mann - Das Mänchen - Das Männlein
Die Frau - Das Fräulein - Das Frauchen
Die Oma - Das Omachen - Das Omalein - Das Omichen - Das Omilein
Der Opa - Das Opachen - Das Opalein - Das Opichen - Das Opilein
Der Hund - Das Hündchen - Das Hündelein
Die Tür - Das Türchen - Das Türlein
Der Präsident - Das Präsidentchen - Das Präsident(e)lein
Die Weltkugel - Das Weltkügelchen - Das Weltkügellein
Mädchen is a diminutive that has lost its basic noun.
Die Magd (maidservant) - Das Mägdelein - Das Mägdchen
Within the last 300 years the 'g' got lost and also the meaning of "Magd" for Woman. So today, "Mädchen" is a standalone diminutive.
The Word "das Mädel" is still known, but only a shortform of 'Mägdelein'. So also diminiutive.
Only in southgerman dialects the basic word can still be found: "die Made" and "die Maid" (for yound women)
Another Example is "Märchen".
Die Mär - Das Märchen
The noun "Die Mär" is nearly extinguished in the german langue. Anybody would say "Die Geschichte".
But "Märchen" is Neutrum, though "Mär" used to be Femininum.
I hope this is helpful to understand the grammatical logic.
-> There is no 'german rule' to degrade a girl to Neutrum!
As the grammatical basic noun for Mädchen got lost, the word is also for the germans no real diminutive any longer. Thats why the DUDEN also allows to use the 'sie' instead of 'es'. Not within the same sentence, but in the next sentece it is allowed to reference with "sie" to "das Mädchen".