As far as I understand, what happened is that Dutch politicians have been too optimistic in their sales for the reduction in nitrogen emissions. In response, the Dutch government has been aggressively making plans to reduce the number of dairy farms in the Netherlands. However, this conflicts with the ambitions of the farmers for two main reasons. Firstly, farmers are very aware of how farming occurs in other countries. The Dutch have a long history of optimizing the farming process with a long history of ever increasing regulations. It makes no sense then to stop farming in the Netherlands to "save" the environment by sending the work to other countries, who then will increase pollution per kg milk produced. For example, farmers in Poland have generally higher maize fields not because they are better farmers, but because they are allowed to put much more manure on the fields. Secondly, farmers are all hard working people who are proud of their family business and who would like to continue their business. Having the government take the business away for controversial reasons doesn't sit right.
Furthermore, from what I hear around me, people are done with the current prime minister Rutte. There have been some scandals including the "Rutte-doctrine" in which Rutte thinks that internal government documents do not have to be shared with journalists and the Tweede kamer (lower house of the Dutch parliament) and him being found out for lying time and time again. The whole scandal around the farmers is just a manifestation of the general civil dissatisfaction, as the BBC points out too.