An axiom is a truth nobody can prove.  For example, everyone knows that one equals one, but there is no formal proof.  However, when one tries to do arithmetic by ignoring that axiom and, say, letting one equal two, then very quickly the math descends into chaos and absurdity.  There is no getting around an axiom, even though one cannot prove it.

A similar principle applies to the social sciences.  It was an accepted axiom of society that men are men and women are women.  No longer.  That axiom has been rejected by some elements of society, and the absurd consequences are becoming more apparent all the time. 

The late Betty Friedan, a so-called pioneer of the radical feminist movement, once said the only difference between men and women is biological "packaging" – that is to say superficial appearance.  It would follow that by changing one's external appearance, one can change his sex.  Liberals accept this as an axiom.

Science clearly refutes this, but radical leftists, and even some conservatives on the more libertarian side, manage to ignore the science, despite growing evidence that the transgender doctrine is harmful to individuals and to society in general.

The science says maleness and femaleness are the two necessary and complementary halves of the human species.  They have different functions that serve each other.  Morally speaking, the sexes are equal but not equivalent, and that seems to be a point of major confusion to liberals. 

To them, equality means interchangeability.  For example, because the races are equal, one can, without analyzing the situation, exchange a white driver for a black driver with zero effect.  The races are not a biological absolute. 

But the sexes are.  Because they are complementary, one cannot exchange a mother for a father.  Indeed, there are many social functions in which the sexes are not automatically interchangeable – for example, physically arduous sports and certain physically demanding occupations involving police work and soldiering.  Even in occupations in which physical strength is irrelevant, women tend to have different preferences from men's.  For evidence, attend any officially sanctioned chess tournament, where gender is considered irrelevant, and one cannot help but notice the predomination of men over women, despite sincere outreach attempts by the U.S. Chess Federation.

Trying to force the facts to accommodate ideology has resulted in attempts to place women into occupations that only in feminist mythology can women serve as well as men.  Army Special Forces is one.  The Army can graduate women in its special forces training program but only by carefully lowering the standards, while maintaining the fiction that they are not doing so.  Carried to its extreme, Special Forces will eventually consist of equal numbers of men and women.  In combat, this will predictably result in catastrophe and defeat.

The absurdities are even more glaring than that.  Consider the case of Mack Beggs.  She is a girl who is undergoing procedures to make her appear to be a man.  In a high school wrestling competition, the testosterone injections Beggs is receiving make her vastly stronger than the other girls, and as a result, Beggs is crushing the competition – indeed, there is no effective competition.  These results help Beggs to outcompete her opponents for a college athletic scholarship.

On perhaps a more sinister note, the morality or immorality of transgenderism is no longer considered a matter of personal opinion.  Now it is a matter of enforced law.  In California and New York, one can be fined or jailed for refusing to address someone by the gender title he prefers, regardless of his actual sex.  

This amounts to a moral standard imposed by the government, which runs roughshod over the First Amendment.  There is, despite the separation doctrine, a state religion: the religion of radical leftist mythology.

Eventually, this could result in something Title IX was designed to prevent: the domination of collegiate sports by men, since the logical conclusion of all this will be to permit men to join women's teams.  Again, the absurdities multiply.

Trying to make one equal two makes arithmetic unworkable.  Pretending manhood equals womanhood will make society unworkable.