The truth of this idea is pretty obvious. Environmental crises are a fundamental part of the history of the earth: there have been sudden and dramatic temperature excursions, severe glaciations, vast asteroid and comet impacts. Yet the earth is still here, unscathed.
There have been mass extinctions associated with some of these events, while other mass extinctions may well have been triggered by subtler internal changes to the biosphere. But none of them seem to have done long-term harm. The first ten million years of the Triassic may have been a little dull by comparison to the late Palaeozoic, what with a large number of the more interesting species being killed in the great mass extinction at the end of the Permian, but there is no evidence that any fundamentally important earth processes did not eventually recover. I strongly suspect that not a single basic biogeochemical innovation — the sorts of thing that underlie photosynthesis and the carbon cycle, the nitrogen cycle, the sulphur cycle and so on — has been lost in the past 4 billion years.
Indeed, there is an argument to be made that mass extinctions are in fact a good thing, in that they wipe the slate clean a bit and thus allow exciting evolutionary innovations. This may be going a bit far. While the Schumpeter-for-the-earth-system position seems plausible, it also seems a little crudely progressivist. While to a mammal the Tertiary seems fairly obviously superior to the Cretaceous, it's not completely clear to me that there's an objective basis for that belief. In terms of primary productivity, for example, the Cretaceous may well have had an edge. But despite all this, it's hard to imagine that the world would be a substantially better place if it had not undergone the mass extinctions of the Phanerozoic.
Against this background, the current carbon/climate crisis seems pretty small beer. The change in mean global temperatures seems quite unlikely to be much greater than the regular cyclical change between glacial and interglacial climates. Land use change is immense, but it's not clear how long it will last, and there are rich seedbanks in the soil that will allow restoration. If fossil fuel use goes unchecked, carbon dioxide levels may rise as high as they were in the Eocene, and do so at such a rate that they cause a transient spike in ocean acidity. But they will not stay at those high levels, and the Eocene was not such a terrible place.
The earth doesn't need ice caps, or permafrost, or any particular sea level. Such things come and go and rise and fall as a matter of course. The planet's living systems adapt and flourish, sometimes in a way that provides negative feedback, occasionally with a positive feedback that amplifies the change. A planet that made it through the massive biogeochemical unpleasantness of the late Permian is in little danger from a doubling, or even a quintupling, of the very low carbon dioxide level that preceded the industrial revolution, or from the loss of a lot of forests and reefs, or from the demise of half its species, or from the thinning of its ozone layer at high latitudes.
But none of this is to say that we as people should not worry about global change; we should worry a lot. This is because climate change may not hurt the planet, but it hurts people. In particular, it will hurt people who are too poor to adapt. Significant climate change will change rainfall patterns, and probably patterns of extreme events as well, in ways that could easily threaten the food security of hundreds of millions of people supporting themselves through subsistence agriculture or pastoralism. It will have a massive effect on the lives of the relatively small number of people in places where sea ice is an important part of the environment (and it seems unlikely that anything we do now can change that). In other, more densely populated places local environmental and biotic change may have similarly sweeping effects.
Secondary to this, the loss of species, both known and unknown, will be experienced by some as a form of damage that goes beyond any deterioration in ecosystem services. Many people will feel themselves and their world diminished by such extinctions even when they have no practical consequences, despite the fact that they cannot ascribe an objective value to their loss. One does not have to share the values of these people to recognise their sincerity.
All of these effects provide excellent reasons to act. And yet many people in the various green movements feel compelled to add on the notion that the planet itself is in crisis, or doomed; that all life on earth is threatened. And in a world where that rhetoric is common, the idea that this eschatological approach to the environment is baseless is a dangerous one. Since the 1970s the environmental movement has based much of its appeal on personifying the planet and making it seem like a single entity, then seeking to place it in some ways "in our care". It is a very powerful notion, and one which benefits from the hugely influential iconographic backing of the first pictures of the earth from space; it has inspired much of the good that the environmental movement has done. The idea that the planet is not in peril could thus come to undermine the movement's power. This is one of the reasons people react against the idea so strongly. One respected and respectable climate scientist reacted to Andy Revkin's recent use of the phrase "In fact, the planet has nothing to worry about from global warming" in the New York Times with near apoplectic fury.
If the belief that the planet is in peril were merely wrong, there might be an excuse for ignoring it, though basing one's actions on lies is an unattractive proposition. But the planet-in-peril idea is an easy target for those who, for various reasons, argue against any action on the carbon/climate crisis at all. In this, bad science is a hostage to fortune. What's worse, the idea distorts environmental reasoning, too. For example, laying stress on the non-issue of the health of the planet, rather than the real issues of effects that harm people, leads to a general preference for averting change rather than adapting to it, even though providing the wherewithal for adaptation will often be the most rational response.
The planet-in-peril idea persists in part simply through widespread ignorance of earth history. But some environmentalists, and perhaps some environmental reporters, will argue that the inflated rhetoric that trades on this error is necessary in order to keep the show on the road. The idea that people can be more easily persuaded to save the planet, which is not in danger, than their fellow human beings, who are, is an unpleasant and cynical one; another dangerous idea, not least because it may indeed hold some truth. But if putting the planet at the centre of the debate is a way of involving everyone, of making us feel that we're all in this together, then one can't help noticing that the ploy isn't working out all that well. In the rich nations, many people may indeed believe that the planet is in danger — but they don't believe that they are in danger, and perhaps as a result they're not clamouring for change loud enough, or in the right way, to bring it about.
There is also a problem of learned helplessness. I suspect people are flattered, in a rather perverse way, by the idea that their lifestyle threatens the whole planet, rather than just the livelihoods of millions of people they have never met. But the same sense of scale that flatters may also enfeeble. They may come to think that the problems are too great for them to do anything about.
Rolling carbon/climate issues into the great moral imperative of improving the lives of the poor, rather than relegating them to the dodgy rhetorical level of a threat to the planet as a whole, seems more likely to be a sustainable long-term strategy. The most important thing about environmental change is that it hurts people; the basis of our response should be human solidarity.
The planet will take care of itself.