What happens worth reflection in The Great Gatsby, Chapters 6-7?
In this section of the novel, Gatsby takes center stage. Nick recounts Gatsby's true past, the formation of his character - both his professional character and his personality - and the novel's conflict between Tom and Gatsby becomes clarified.
After the reader becomes familiar with the exact circumstances of Gatsby's dream and his attachment to Daisy, Daisy finally comes to one of Gatsby's parties. After this point, Gatsby's intentions are clear and soon are at odds with Daisy's sensibility.
When Gatsby visits Daisy and Tom in New York, Gatsby presses Daisy to renounce her marriage and her love for Tom. To do this would mean, effectively, that Daisy would be saying her entire adult life has been meaningless. This is what Gatsby demands.
It is part of his vision for beginning a new life by recapturing the past. The interim between his first meeting with Daisy and this one must be somehow erased or rendered null. Daisy is unable to take this step. Her vision is one of romance, not one of time-travel.
She cannot nullify her life, even to gain access to her own dream of true love.
The novel reaches its climax in this section. Myrtle is hit by a car. The relationships between Gatsby and Daisy and between Daisy and Tom are decided. The character of each is given final articulation.
This articulation, for Daisy, is one of surprising weakness. Where she had been prepared to be bold and to strike out on her own with Gatsby, when the moment arrives she wilts. This is at least partly Gatsby's fault.
Gatsby proves that he is not entirely unlike Tom. He is demanding and insistent on his own welfare (at the expense of others). This is clear in the flashbacks as well as in the scene taking place in New York.