Saying that this sketch is "the most dangerous graphic" is not an overstatement. The tree of evolution is a central element in the structure of what the philosopher Daniel Dennett once called "Darwin's Dangerous Idea", title of one of his books. Darwin's insight was not just that species evolve, though. Many thinkers before him (his grandfather, Erasmus, among them) already knew that. What Darwin did was to uncover and thoroughly explain the mindless mechanism behind such a process: natural selection, the non-random filtering of inherited traits by environmental pressures. This was threatening for many at that time: if a biological algorithm can explain how life changes, what do you need a conscious, almighty designer for?
I was reminded of Darwin's sketch, and the danger it posed to those prone to myth, fairytales, and obscurantism, while reading The Hockey Stick and the Climate Wars: Dispatches from the Front Lines, by professor Michael E. Mann. Mann describes the smear campaigns built against him and many of his peers by a well-funded herd of bloggers, pundits, and fringe politicians and academics that will not accept that climate change and global warming are pushed by human activities, no matter how strong the evidence has grown.
Mann's ordeal reads as a reenactment of the tactics used to fight against the teaching of evolution and against the links between tobacco and lung cancer in the past. I recommend you to take a look at the book: it is a cautionary tale about how easily misguided mainstream media can be when they try to give voice to "both sides" of a "controversy", granting merchants of doubt a credibility they don't deserve. There's not really a controversy here: today, considering all the data that have been gathered and all the research that has been done, giving equal space to scientists and deniers is like teaching alchemy as an alternative to chemistry in schools.
What climate change deniers have attacked with most intensity throughout the years is not Mann's research and data, though, but his most iconic creation: the hockey stick graph, originally published in 1999, and reproduced by the 2001 Third Assessment Report of The Intergovernmental Panel on Climate Change (IPCC). Another most dangerous graphic that has been proved right several times, albeit with nuances and tweaks (for a summary, read this). As in the case of Darwin's, reality is there for you to see, even if you don't want to see it.