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Waitbutwhy put it well: “ 18,000 years ago, global temperatures were about 5ºC lower than the 20th century average. That was enough to put Canada, Scandinavia, and half of England and the US under a half a mile of ice”

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That's not really helpful, when you think about it: Are the effects linear? How much ice would the US be under for temperatures of 1°C below 20th century average? A fifth of half a mile? No ice at all? And what does that imply for 2°C above? 0.2 miles of ice below the surface?

I prefer actual predictions of the effects, not bad analogies or useless data points.

Sure, it's unhelpful if you're trying to build a model or understand the science, but 90% of people aren't; and it's accurate –if unhelpful– analogies like this that get those people onboard.

The point is to show that the system is very sensitive, and that the folk wisdom of "2 C is just 2 C what's the big deal?" isn't valid.

Then why not just explain to people the predicted consequences of a 2°C temperature increase?

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