The role of nature documentaries in shaping public attitudes and behaviour towards conservation and wildlife issues is unclear. We analysed the emotional content of over two million tweets related to Our Planet, a major nature documentary released on Netflix. We show that tweets were largely negative in sentiment at the time of release of the series. Further analyses revealed that this effect was primarily linked to the highly-skewed distributions of retweets and, in particular, to a single negatively-valenced and massively retweeted tweet. We also compared the sentiment associated with species mentioned in Our Planet and a set of control species, with similar features but not mentioned in the documentary. Species mentioned in Our Planet were associated with more negative sentiment than the control species, and this effect coincided with a short period following the airing of the series. Our results are consistent with a general negativity bias in cultural transmission, and document the difficulty of evoking positive sentiment, on social media and elsewhere, in response to environmental issues.