You failed to distinguish the concepts even in your own terms; a girl is a person, and a burger isn't, and you need to know that to form a grammatical sentence about them.
Even though a girl is a person the gender of a girl (das Mädchen) is neuter in German. You need to know that grammatical gender to form a grammatically correct sentence - you do in fact need to say "it" ("er") in your sentence referring to the girl you met yesterday.
A girl is person and a burger isn't, but in German a girl is an "it" and a burger is a "he".
Taking sex-based gender distinctions for our example, we can observe that Chinese speakers aren't able to correctly choose between the English pronouns he and she, despite the fact that this distinction isn't arbitrary in the slightest (and Chinese speakers routinely make it themselves in other contexts!). The reason is simply that their native language doesn't make the distinction, not that the distinction is theoretically difficult to make.