The right to play sport fairly and safely is universally recognized. Consequently, there have always been regulations about competition in which people may compete - Male, Female, under-age, certain weight groups, etc. The female category has been traditionally open only to biological female athletes. Recent societal shifts in gender theory proclaim gender as a fluid concept, saying that a person's gender identity has greater importance than birth sex. Transwomen athletes, born male but identifying as women, demand it is their human right to play in the female category. Following IOC guidance, many sports assented to the change. This means that in a physical contest, biological females are pitted against one special group of biological males, those who identify as women. Female athletes who miss team selection or lose to a transwoman have no other category in which to play. Can transgender inclusion co-exist with fairness, physical safety, and integrity in women's sport? Is erasure of purely female achievements and records acceptable? Are rewards, fame, affirmative programs, and sporting careers for females not important? Does authentic female sport cease to exist? What are solutions? This text presents the bio-physiological-sport science research that dismantles the myth that there is no performance advantage of transitioned transwomen athletes. It also explores the legal framework protecting sex-divided sport. The focus is on elite competition. There are also implications for grass roots and pre-pubertal children in sport. This text provides essential background for athletes, sports administrators, the public, and LGBT+ communities to debate this hot button issue with openness and respect.