When you're arguing on an online space large enough for a position that doesn't yet have overwhelming support, you're always going to get some pushback of some kind. It's never going to be completely pleasant. The silver lining is that, if you're arguing for your positions well enough, you're going to bring some more people to your side each time. Many of them will not be vocal, many of them will have to meditate of what you've said, for many of them it will just be a fleeting thought, but it might be a stepping stone that leads them to actually change their mind in a later discussion. I have this mindset because it's coherent with how I've changed my mind over the years after engaging with different people, and so, when I'm advocating for something on a space that isn't overwhelmingly welcoming (which might usually be autism advocacy, anti-capitalism, secularism, depending on the site), and I'm in a tempered mood at the moment, I immediately assume that I'm going to get pushback even on things that I'm objectively correct, but that doesn't mean I'm not making useful progress, so I should argue with more charitability than I think the other person deserves.

On the gender issues topic specifically. Discounting a minority of people whom you're never going to make see reason, your goal is to make your positions understandable to the men who either don't have a strong opinion yet or are only mildly hostile. I'm going to use the example of an user I saw the other day out of memory: picture a man who has had an aggressively mediocre life: few meaningful relationships if any, no romantic or sexual partners, hating his job or whatever it is he's studying, he hasn't (or hasn't seen himself having) acted particularly mean towards anyone in his life but he has particularly vivid memories of women or girls provoking him pain (be they a rude teacher, an abusive mother, high school bullies, or whatever). Now picture him reading these two messages:

(...) Life feels very unsafe to me. I have been catcalled, had my opinions dismissed and driven out of spaces I wanted to be in ever since my teens, (...) There are always some men who make the world a dangerous place for me.

and

(...) Life feels very unsafe to me. I have been catcalled, had my opinions dismissed and driven out of spaces I wanted to be in ever since my teens, (...) Men make the world a dangerous place for me.

I've made the nuance very obvious here, but it will usually be far more subtle. Sometimes it will be someone not making their position as fair and impartial as possible, sometimes it'll be that they literally do not realize their words might be misinterpreted, but a good chunk of the individual shitshows I've seen in the past few days here are easily understandable if I picture someone saying: "I've been a sad shit for my whole life without harming anyone, and if anything, I've been treated unfairly. And now you're telling me I'm the culprit!?", and the difficulties of this guy through his life might have been several degrees less severe than your own, but if he's misunderstood what you're saying, or the message he's read is less charitable, or if the person he's just read has been perfectly reasonable, but five minutes ago he's read a different message from someone else who hasn't been, which twists the context, he isn't entirely wrong, because he was minding his own business but now he feels accusations fall upon him out of nowhere.

On the bear argument specifically. Ignore the goddamn bear. You can make a lot of good arguments about why choosing the bear is wrong, and this derails PLENTY of discussions that could otherwise be useful and meaningful into a stunlock where one side wants to argue about why some people choose one way, and the other about the specific hypothetical. Don't go into "(...) and that's why I'd choose the bear", ignore the metaphor, redirect the conversation in an useful direction, such as the actual living experiences of women, what kind of society would you want to see and what kind of specific changes would you like to see people make.

This advocacy is almost never going to be completely pleasant. This isn't a justification, or discouragement, it's just acknowledgement of the fact that plenty of people are going to be predisposed against your position, or skeptical, or outright hostile, and you personally are not going to see the fruits of your own, individual, specific labour, because whatever useful progress you make will be brewing on the background. Plenty of people whom you've made think will perhaps upvote you at best, but very, very few will admit "You've completely changed my mind on this", but that doesn't mean what you're doing isn't useful. Sometimes you won't make the perfect argument, because you don't have the exact perspective of what the other side is thinking, and because no human is omniscient, and you might have to rethink nuances, strategies and approaches, but engaging other people with the ultimate goal of creating a society where everyone is accepted in equality and freedom is always, on the long run, worthwhile.