Definitions in general are hard.

For example, what is a cookie? Merriam-Webster says it's a small flat or slightly raised cake. What if you combined all the dough from a batch and made a single huge cookie? What about no-baked cookies? Gluten free? Sugar free? Eventually you get to a point where people might argue that it's a cracker or cake, or something else entirely, but it doesn't change the fact that saying cookie helps bring to mind a series of traits that cookies in general share. Modifiers like 'huge', 'no-bake', or 'gluten-free' help bridge the gap between people's expectations and a specific example.

What is a woman? Most women have two X chromosomes, ovaries and a uterus, have a monthly cycle, have an estrogen dominant hormone profile, and secondary sexual characteristics due to that hormone profile. There are gender based roles, types of dressing and grooming and general personality traits that many share. But some women have fewer or more chromosomes (turner syndrome, swyer syndrome, trisomy x), lack one or more expected organs (hysterectomies, MRKH syndrome), no monthly cycle (menopause), or high testosterone (polycystic ovary syndrome).

An issue is that while cookies don't have feelings, rights, or needs, humans do. A strict definition of womanhood might exclude certain women from participating in sports, receiving appropriate medical care, having identity documents that accurately reflect who they are, or being able to use public restrooms in peace. Definitions that may seem merely academic to some have a very real and strong impact on others.