Title reference: the cooperation between Sheldon and Amy, which fluctuates between working together and insulting each other.
Sheldon is very happy with Amy's list of fair topics for insult, which include educational pedigree, scientific field and intellectual prowess. Not surprisingly, these happen to be the areas where Sheldon excels at: he often belittles Howard's engineering education, has nothing but contempt for geologists, and constantly questions Leonard's intelligence.
Sheldon says that he is bothered by how birds look at him, another reference to his fear of birds that was established in The Friendship Algorithm (2009). The fear undoubtedly stems from a childhood experience where he was chased into a tree by his neighbor's angry chicken, as first mentioned in The Jiminy Conjecture (2009).