There may be a few reasons why Harper Lee chose to do this. Part 1 talks about Jem and Scout when they are children, while Part 2 talks about them as adults. Part 1 is able to show the perspective of the children towards Boo Radley. Part I shows the development of the children towards respecting their father. The most important part of Part I is that Dill, Jem, and Scout seems scary to children.
Part II of the novel is about the Jem, Dill, and Scout as adults. The main issue is racial discrimination and it seems that everything that Attiticus has worked to teach his children has been lost.
So, there are a few main reasons why she would break the novel into two parts. One is that there is a natural division between childhood and adulthood. Another reason is that this allows there to be two climaxes in the novel. Part I seems to be focused on character development while part II is focuses on the theme of racial discrimination.