If by that you mean that there is a binary concept, such that ever person is either a man or a women, then even in the purest biological context context that isn't true as there are all sorts of examples of intersex condition which involve individuals exhibiting biological characteristics of both men and women.
As Jeremy P pointed out previously the most 'correct' biological definition of male vs female is about production of gamete of particular size - yet even here there are examples of individuals who produce both male and female gametes and others who produce neither.
So even in the context of pure biological sex, man vs woman isn't a pure binary concept.
Of course in terms of trans-gender people we are talking about gender rather than biological sex (the key is in the name) and in that context there is a much wider spectrum of individuals who in gender terms (biological, psychological and cultural) identify to a greater or lesser sense with characteristics that we typically ascribe as masculine or feminine.
Your last para is the one that seems to have no answers and generates only confusion, which is why competitive sports should not be segregated based on gender, unless you can explain how gender plays a role in unfairly disadvantaging people in competitive sport.
What are the characteristics that we typically ascribe as masculine?
What are characteristics that we typically ascribe as feminine?
Who decides which category - masculine or feminine - that a particular characteristic falls into in any given year? The IOC?
Does it not make more sense for the IOC to just stick to looking at the stats supported by science as to what confers unfair advantages in sport, rather than worrying themselves about subjective abstract concepts, which people can't agree on because there is no supporting objective evidence? So Hubbard regarding herself as a woman is irrelevant for the purposes of competitive sport as there is no objective evidence for the gender category "woman".
