I will go through a few examples to try to find, with you the reader, some of the limits that are involved here. You have to decide which of the two options you'd prefer. The numbers in the first few examples are not approximations of real odds. They are thought experiments. Some better approximations come later.

So…

Where is your limit?
It is now upon you to decide where your cutoff is. Even at 10x more likely than normal daily chance you'd probably still rather take that than the bear. But when does that stop? It might be useful to really think this through and think about where on the scale you'd go, and where too much is too much for you. Of course any of the rape chances above daily normal chance are too much if repeated multiple times, but this is a one-off thing. Whatever you choose happens once and then, if you didn't die, you go back to the rest of your life with normal daily rape chances.

The other question is, how dangerous really is a man? Like, what's the actual statistic for the likelihood of a man just sexually abusing a woman if they happened to meet in a space devoid of help and witnesses, ie. devoid of accountability?

All of us are going to find very different estimates here. Personally I think that a woman could probably go through at least 1000 men before finding someone who will actually sexually assault her. Of course many more men are going to be indecent or abusive towards her before that (which is shocking in its own right), but I think the overwhelming number of men won't do anything life-changing to a woman even in a space with no accountability. You might, and probably will, come up with your own calculations here, but I personally would put the chance at 0.1% and, while maybe not a good number, I would not think of it as utterly unreasonable either.

What we do now from here to reach a conclusion is easy. Where is your cutoff, where is your expected chance, and is your expected chance above or below your cutoff? Now in my case, my calculation would go roughly like this: For me, 10% risk of getting raped is too much. I know that with a 10% (or less) chance of it happening, I'm comfortable enough with my odds. The previously established 0.1% are below 10%. So, if 10% is the highest amount of risk I'm willing to go with then I'm perfectly fine with 0.1% and the correct answer to the original question is indeed man.

For some extra flavor we can also use the bear chance as a coefficient. Since I'm not guaranteed to die to the bear I can be cocky and reduce the limit of what I'm willing to take. If I take a 20% bear chance (ie. 1 in 5) then I can divide my limit like this: 10ppt / 5 = 2%.
I think this is reasonable because the bear chance matters in the chance calculation. If I am willing to accept risks with the bear then I can afford to accept less risk with men. In my case, 0.1% is still well below 2%, but this might change something for you.

The cool thing is that we can use the above-established framework to explain what women's real problem with men's justification of the Man or Bear question is. Some of the properties in this model are fixed. Whether you used the same numbers as me, the bear chance and the chance of getting raped are just fact numbers. Even if we estimate them differently, that is only because we all work with different information and have different guessing skills. But, the one thing that will be different between everyone's mental model of the formula is the limit, the amount of risk a person is willing to take before they'd rather take the bear.

This limit is, to a degree, informed mathematically, but for many (especially women) it will be an expression of their fear. While there may truly be a rational, mathematical solution to the problem, people who are afraid of things will naturally try to avoid falling victim to it. Even within women, the reported limits will differ from one person to the next and they are exclusively a measure of how afraid they are of men. For some women this limit might be above the actual odds, for some it's below, for some it's right on.

It doesn't really matter. The online phenomenon here is the fact that many women, upon hearing the original question, were reminded of the fear that men cause in them and chose the bear because of it. Men do not know this fear, so for them this inevitably becomes a matter of statistics. As far as my understanding goes, for women this discussion is not about statistics, whether their assumptions are right or even that many women choose bear; this discussion is about the fact that, for men, unaware as they are, this discussion so often does end up in statistics. They do this because they do not know the fear, and they have no other way other than to tackle this question statistically.

In fact, that was my reflex too and it forever will be. Considering that men do in fact not have these experiences to draw from to inform their man or bear decisions, it will be very hard to try to use it to teach men that they are scary. Now personally I don't need to be told that I am conceptually capable of overpowering most women, I know that and I don't plan to actually do it. I also know that this means that most women unfamiliar with me won't trust me, because they can't. I guess the point of this question is that many men do not? And yes, most men are decent to women, but the point is that many men do not, a reality that is actually so common that unlike rape, male indecency towards women is a daily occurrence (I mean, women are raped every day, but not every woman is raped every day. But every woman does become victim of male indecency on a daily basis.)