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It's very difficult to create those spaces without being overrun by the toxic misogyny you're specifically trying to discuss and avoid. On the other hand, it's perfectly acceptable to simply discuss those topics in public. Women's liberation was successful not because women had safe spaces to discuss it, but because it became part of the popular discourse. Damaging gender norms and societal expectations were ever-present, and women were forced to challenge them everywhere.
Simply put, men don't face the same levels or types of discrimination. That doesn't invalidate your experiences as a man. It just means you have to be sensitive to the perception of your message.
It also means being your own sheriff when it comes to the toxic side of our gender. We have to call out misogyny when we see it, and reject hateful bigotry that is frighteningly common in these discussions.
Women's liberation was not a liberation from men, but a liberation from patriarchal society that placed women below men (coincidentally run my self-serving men). Men's liberation is liberation from the exact same society and the same gender-biased expectations and pressures. They are different expectations, and different severities, but while the enemy is the same, a collection of ideas, the enforcement is entirely different.
For women, it was very often an actual group of men that they were fighting, and the fight was frequently violent. Recognizing that our struggles are analogous but not equivalent, it's going to be important to stay on topic and not devolve into hate and whining.
But when those topics arise, get involved. Talk about mental health, feelings of isolation, parental rights, social pressures and anxiety, and intersectionality. Don't go looking for the safe place to have the conversation, make all spaces safe for the conversation to take place. We're going to have to be pioneers on this one, because the previous generation was fairly inept at such efforts.