(throwaway for obvious reasons of the culture war. /sigh)
One example might be the Isbister v. Boys' Club of Santa Cruz case, in which the Supreme Court of California ruled that, according to civil rights laws, no space could be legally barred to women. (imagine that same justification banning women-only spaces; it simply wouldn't happen, because of course it wouldn't).
Or, more famously, Earl Silverman's attempt to open a shelter for male domestic abuse survivors in Canada, for which he was ridiculed and ostracised and eventually, when the government refused to fund such a thing (male domestic abuse victims? Perish the thought!) had to shut it down, ending his own life in despair. Erin Pizzey, who founded the first women's shelters in the UK, faced similar harassment (including bomb threats serious enough that the police decided that they needed to intercept all of her mail to check it for explosives) when she began discussing the same thing, and was eventually driven out of her home country.
In fact, the dearth of male-focused help in general, even in situations where men are the overwhelming majority of the at-risk population. See, for example, homeless shelters in the UK. Ironically, some women in need of assistance escaping their abusers sometimes get turned away from these places because they come with male children.
Generally speaking, most "assistance" actually primarily aimed at men treats them like shit. See, for example, the Duluth model, the most common batterer intervention program in use in the United States. It explicitly pre-concludes that any domestic dispute is caused by men trying to dominate women. Ellen Pence, its creator, has even gone on record stating, "By determining that the need or desire for power was the motivating force behind battering, we created a conceptual framework that, in fact, did not fit the lived experience of many of the men and women we were working with. [...] Speaking for myself, I found that many of the men I interviewed did not seem to articulate a desire for power over their partner. Although I relentlessly took every opportunity to point out to men in the groups that they were so motivated and merely in denial, the fact that few men ever articulated such a desire went unnoticed by me and many of my coworkers. Eventually, we realized that we were finding what we had already predetermined to find." (emphasis added) This has not lessened its popularity as an intervention mechanism for domestic disputes.
I mention this not as an example of a male-only space being destroyed, but as an example of why they may be needed. Many men, emotional illiteracy aside, do in fact realize when the chips are stacked against them. They do not learn to socialize with other men in school, nor in the manner that men have historically been socialized. They are allowed in the public forum, but most attempts to share their perspective, at least in the more woke circles, are met with hostility - after all, they are the historical beneficiaries of the social order, and therefore they cannot also be allowed to be even perceived as victims, especially when being a victim confers social status. No matter that "privilege" is not uniformly distributed.
Philosophically speaking, men ought to have a male-only space if only for the benefit of being able to calibrate themselves against other men, rather than having to constantly downplay their own difficulties and miseries by the standards of women; a man ought to be able to feel bad about losing his job without having to also remind everyone that he still has it better than a woman who would be jobless and also facing sexism. He ought to be able to exult in a promotion or other achievement without "checking his privilege" and feeling guilty about how his success closes the doors for others who have not had the opportunities he has.
If men should be more emotionally intelligent, they need a safe space where they can express their emotions. It has become abundantly clear to many of them that gender-integrated spaces are not safe, for the same reason that I'm posting this comment from a throwaway account.