In Chapter Six, why is the phrase "even the pigs joined in at critical moments" important?
The completion of the windmill, at this point, seems to have become an absolute necessity. Once Napoleon claimed that the idea to build it was his, it became imperative to follow his instruction and tackle the task. Since it became so important, everyone felt compelled to pitch in. Collecting the limestone and breaking it into manageable pieces was an extremely arduous task and that is why the pigs joined in at critical times.
The fact that the pigs were actually prepared to perform physical labor indicates the significance of completing the project. They had, up to this point, not performed any physical work and were supervising and doing administrative tasks, the "brain work," which they claimed was essential for the smooth running of the farm. There is greater significance in the fact that they, through this action, showed that they shared, to some extent, a common purpose with the rest of the animals.
Once the windmill was completed, all would benefit. The pigs realize that when everyone benefits they, being the most superior, benefit the most and continue living lives of privilege. It is for this reason that they are obviously keen to help—the sooner the task is accomplished, the better for them.
To put this phrase into context, it appears in Chapter Six of Animal Farm when the animals are working harder than ever to finish the windmill. From the point of view of the narrator, this phrase is significant because it provides the reader with an example of bias: the narrator is clearly suggesting that the pigs rarely do any work and, when they do, it is only at moments which they deem to be "critical." The narrator is also foreshadowing the pigs' increasing separation from the other animals, particularly that of Napoleon, who rises to become the farm's absolute ruler.
In contrast, however, this phrase is also important because, up to this point in the novel, the pigs have acted as the leaders of the farm and differentiated themselves from the workers. Their sudden involvement in the building of the windmill demonstrates a rare instance of good leadership and a sense of community spirit.
Up until this point, the pigs have separated themselves from the workers in order to be leaders and supervisors. The fact that they are doing some actual manual labor shows how important everyone feels the completion of the windwill is.