I don’t think the hypothetical comparison with an asteroid strike works, not least because you deflate the probability in the story. Climate change, meanwhile, has a range of probabilities all of which are significantly greater than zero and therefore the two aren’t comparable. Furthermore, if someone is in total denial about climate change for political and financial reasons, providing a false analogy won’t change their attitude.
Our fundamental problem is that the human brain isn’t evolved to do much thinking ahead and has zero capacity for dealing with large-scale issues. We evolved to cheat our neighbors, learn how to shape flint, and work out how to impress the person we want to copulate with. The fact that a tiny number of clever people over the years have developed amazing technologies shouldn’t blind us to the fact that the vast majority of our species are little more than apes stroking smartphones. Thus tackling an existential problem is pretty much out of scope for the human brain, especially when to do so would conflict with the short-term priorities of many.
I wish I could be more optimistic about the probability of doing something meaningful about anthropogenic changes to the Earth but so far I have no reason to be anything other than deeply pessimistic.