I don't see how it is broken, unless you impose a particular definition on it and then say "look it doesn't fit the definition". Hurtful, sure.
Broken, in this sense, means wrong, non-functional, does not fit reality.
For the many reasons I explained. To grossly exaggerate to make my point: a definition that claimed gender is defined as to whether you wear lapels that open on the left or right would be broken. Yes, there is often a close relationship between how one's lapels open and one's gender (at least in the USA). But the lapels in a very real sense do not define the gender. You appear to be stuck on the concept that the genitalia alone define the gender. This too is a broken definition. Genitalia often relate to gender, but here too there exist poor matches. This is not just some attempt to fit a political agenda: it is a biological fact in many animals: gender, in a very real sense, is much more complicated than the shape of one's genitalia at birth, is not a simple binary, and takes into account multiple aspects, including how one's brain is wired to think of one's identity.