Bluntly, I wouldn't want to have some lady I've never met, trapped in the forest with me either. Not because I'm a bad person, far from it.
I feel like I'd be rather handy if I was lost in a forest, but she wouldn't know that.
Fact is, any lady weighing in on the discussion doesn't have any reasonable guarantee or even a reasonable probability of getting someone half as helpful as me, and a nontrivial chance of getting a date rapist, so I get it. The worst that a bear would do is kill and eat them, and if they're lucky, it'll happen in that order. There are fates worse than death.
I don't take any offense at someone answering "bear". At all. It's an age old question, of the devil that you know, versus the devil that you don't. Sure, there's a non-zero chance you'll end up in the woods with bear grylls (or someone with a similar skillset), or Mr. Rogers (or similarly kind person), but the far more likely scenario is not that.
It's not a statement against me personally as a male, it's a statement about the average man. If that offends you, there's a good chance that you're part of the problem.
I'm not here to judge. So I'll let you decide for yourself.
The fact is, unknown men is basically a gamble most aren't willing to make. What can we do about it? Probably somewhere between Jack and squat. Unless we can "fix" the socially inept and creepy men, as well as the rapists, would-be (opportunistic) rapists, date rapists, and just all around shitty men, pretty much all at once, this stereotype isn't going anywhere. Just be the change you want to see in the world, and try to encourage your brothers to be better.