I would argue that "male" and "female" can be subjective socially constructed categories in certain contexts. For example, intersex people exist, people with hormone conditions exist. Whether these people are male or female is a very hairy and nuanced conversation that is viewed on a case-by-case basis, and sometimes creates controversies, such as women who have XY chromosomes and naturally elevated testosterone being disqualified from competing as women in elite sports.

See: Caster Semenya, who is disqualified from competing as a woman because she has XY chromosomes and naturally elevated testosterone. She's intersex. Her only supposed recourse is to take medication to force her testosterone levels lower to be qualified as a woman. Of course, the organization is now defining who counts as a woman to qualify for women's sports is likely making socially constructed categories.

Right, but the existence of edge cases does not mean that the "male" and "female" labels are completely arbitrary.

The words "bed" and "sofa" aren't arbitrary social constructs just because sofabeds exist.

Your comment merits a more thoughtful reply than this, but I discussed the same issue here some months ago (https://news.ycombinator.com/item?id=26876186) and it's hard to work up enthusiasm now.