I apologise if this thread has become off topic as it was supposed to be about Transwomen and it seems to have ended up being about whether sex discrimination exists, but I want to follow up a few of Snorlax512's points:
Based on what?
Your best shot at institutional sexism against women (and I mean blatant sexual discrimination) is the wage gap, which has been either completely debunked or reduced to a value of at most 10% after accounting for multiple controls. This probably disappears after measuring for every single factor (such as men are more likely to ask for promotions etc...)
Political and economic institutions in the United States and globally are dominated by men - these are the institutions whose decisions and influence dictate and direct the political economy:
US Congress:
80% male, 20% female
State Legislatures:
only 24.4% women
Notice also that the lower the proportion of women in the legislature, the more likely that state is to have restrictive abortion and reproductive rights laws:
http://www.self.com/story/these-6-maps-show-the-insanity-of-abortion-restrictions-in-the-u-s
President's of the United States:
100% male
Courts:
Women are still vastly underrepresented
CEO's:
only 14% women
And disparities within professions:
http://dpeaflcio.org/programs-publi...-at-occupational-obstacles-and-opportunities/
The gravity in these matters is also extremely great - women are largely shut out of positions of political and economic decision making but still bare the brunt of many of those decision - States with Republican and male dominated legislatures have passed abortion restriction that really only impact women.
Sentencing disparity (pretty much indisputable: men are sentenced 60% longer for the same crime, females are twice as likely to avoid incarceration if convicted.)
Which as I highlighted earlier is not necessarily unjust when you look at disparities of impact prison has on women compared with men - you said you wanted to account for factors?
Reproductive rights: women have the choice of abortion whereas men are forced to pay child support no matter what. He takes responsibility for the woman's decision and has zero say over the matter.
Not a fair comparison. Being forced to physically go through a pregnancy and give birth is not the same as being required to pay child support. Control over one's body is vastly different to a wallet.
In addition it's debatable whether it's just for a fathers not to have to pay child support where the result is the child will be forced to grow up poorer or in poverty.
The best argument I can find to debunk this may be the legal one - You're argument was rejected by both the district court and the Sixth Circuit in
Duaby v Wells:
The plaintiff's claims have been rejected by every court that has considered similar matters, and with good reason. The plaintiff's suggestion that the support provisions of the Michigan Paternity Act implicates the Equal Protection Clause does not find support in the jurisprudence. First, the Act's provisions apply only if a child is born and essentially do not concern anyone's right to choose to be a parent. Second, the statutory provisions are facially neutral, requiring both parents equally to support the child. Third, the plaintiff argues that enforcing the Act's provisions, without any deviation from the neutral language of those provisions, still can implicate the Equal Protection Clause because of an underlying inequality: the State's recognition that women can choose to be parents and men cannot. This argument in turn is based on the existence of a right supposedly grounded in substantive due process, as the plaintiff acknowledged at oral argument. But the Sixth Circuit has squarely rejected the argument that fairness or reciprocity generates a substantive right to avoid child support on the theory that a woman has the right to bring to term or terminate a pregnancy on her own. Finally, the plaintiff has failed to demonstrate in even the most remote way that state action plays a role in the interference with his choice to reject parenthood. The consequences of sexual intercourse have always included conception, and the State has nothing to do with this historical truism. Because the plaintiff has failed to state a colorable claim in his amended complaint, the Court will dismiss the complaint against all the defendants. In addition, the Court finds that the plaintiff's claim is frivolous, unreasonable, and without foundation. Therefore, the Court will grant the State's motion for attorney fees under 42 U.S.C. § 1988(b).
https://casetext.com/case/dubay-v-wells
And Critically from the appeal case
Dubay’s claim that a man’s right to disclaim fatherhood would be analogous to a woman’s right to abortion rests upon a false analogy. In the case of a father seeking to opt out of fatherhood and thereby avoid child support obligations, the child is already in existence and the state therefore has an important interest in providing for his or her support
http://www.opn.ca6.uscourts.gov/opinions.pdf/07a0442p-06.pdf
The discussion of the 14th amendment arguments concerning the Michigan paternity statute are interesting. The 6th Circuit seems to have essentially "bench slapped" the argument.
Custody, as mentioned by Satoharupika.
This is also due to other factors.
For a start, only about 4% of cases actually make it court:
http://www.huffingtonpost.com/cathy-meyer/dispelling-the-myth-of-ge_b_1617115.html
For another, in the majority of cases where fathers apply for contact orders, the orders were successful:
http://www.nuffieldfoundation.org/s...es/Executive Summary with full disclaimer.pdf
http://www.nuffieldfoundation.org/sites/default/files/files/Full report.pdf
Thirdly, the governing principal of family orders is the best interests of the child:
https://theconversation.com/child-custody-parental-rights-vs-the-childs-best-interest-33620
A lot of so called fatherhood groups who claim a bias against them exist work on their presumption that their rights are more important than the child's:
http://everydayfeminism.com/2013/08/bias-against-fathers/
Or how nurses can't be male and if they are, they must be gay or feminine. There are still societal roles that men aren't supposed to lurk into. Like girls can be tomboys and like certain boy stuff but guys can't be girly and show their feminine side or else they'll be mocked by peers. I feel like most industries are male run and men's issues are an underlooked value in equality. But this doesn't mean that feminists should be painted as batshit crazy radicals when that's the vocal minority and many people believe in women's rights but don't call themselves feminists.