Because its a diminutive form of "die Magd" (the maid), that a long time ago became the official word for "the girl", -chen and -lein are sufixes for diminutive (adding an Umlaut in some of them), and ALL diminutives are neuter: der Hund/das Hündchen, das Buch/das Büchlein, die Frau/das Fräulein...
For whatever reason Madchen (apologies for the lack of umlauts, can't do it with my keyboard) is a neutral noun and not a feminine noun (even though Junge is masculine, which I agree is confusing). It's good to know though that whether a noun is masculine femenine or neutral doesn't always necessarily correlate with if the noun ACTUALLY represents something masculine or feminine or whatever.
So, how do you differentiate 'isst' and 'ist' in a conversation. Some Germans speaks very quickly. Of course if they mention 'Essen' or some piece of food, then that could help. Example: Das Madchen isst eine Tomate OR Das Madchen ist eine Tomate. Clearly, the girl is not a tomato, but I could see that it could be confusing hypothetically.