I think perhaps the difference is that while in English it's people that have gender, in German it's the words that have gender rather than the things that the words refer to. Each of these words might refer to the same thing:

* Mench (masculine): human being

* Person (feminine): person

* Geisel (feminine): hostage

* Mädchen (neuter): girl

The pronoun used to refer back to a noun is often the one that matches the gender of the noun rather than the gender of the person that the noun refers to.

(French also has the feminine noun "personne", which I think you can refer back to with the feminine pronoun "elle".)