Why does Butterfly allow Pinkerton to abuse her?
This is a great question. However, some reflection will help tremendously. Culture certainly has a role to play here, as Japan traditionally espouses a submissive role to women in society. So, when Pinkerton, not only a man, but a foreign man with authority and power, enters into a relationship with Butterfly, there is a commonsense submission that Butterfly shows. The whole relationship is rooted in inequality.
Another important consideration is the age of Butterfly. She is only fifteen years old. This is probably the most significant point to keep in mind. She is only a girl. She is infatuated with B.F. Pinkerton. The age gap causes trust and subservience. In short, all structures of power are on Pinkerton's side. The only power that Butterfly sadly possesses is the power over her life. So, in the final act, she does what she has the power to do. She commits suicide.