There are three reasons why To Kill a Mockingbird was set during the Great Depression: everyone was poor, racial and class tensions were high, and that was when Lee was a child.
The Great Depression was a time of universal suffering. Everyone was poor.
Atticus said professional people were poor because the farmers were poor. As Maycomb County was farm country, nickels and dimes were hard to come by for doctors and dentists and lawyers. (ch 2)
This allows Lee to insert the Finch family as an equal to everyone else. No one in Maycomb is better off. Mr. Finch is therefore more of a moral guide, because he does not stand above the others.
The Great Depression was also a time of great tension. Since the story in To Kill a Mockingbird centers on both class and race, it was set during a time when these tensions were especially high. An example of this is the difficulty that Scout has in getting their teacher to understand that Walter Cunningham doesn’t have money to borrow lunch.
He didn't forget his lunch, he didn't have any. He had none today nor would he have any tomorrow or the next day. He had probably never seen three quarters together at the same time in his life. (ch 2)
Although it’s possible that Lee wanted to make an impact on the civil rights movement while also distancing the story by setting it in the past, the greatest evidence of why the book was set in the 30’s is that this is when Lee would have been a girl. She was born in 1926, which puts her just about exactly as old as Scout was over the course of the story.
Although Lee swore the book is not autobiographical, she definitely drew on her experiences.
Maycomb was an old town, but it was a tired old town when I first knew it. In rainy weather the streets turned to red slop; grass grew on the sidewalks, the courthouse sagged in the square. (ch 1)
Most people believe that the town of Maycomb is based on her hometown of Monroeville, and the character of Dill is based on Lee’s friend Truman Capote, who came to stay with Lee’s next door neighbors in the summer. The similarities are striking. Lee was also a tomboy, like Scout. Lee also went to law school, though she dropped out to write this book.