Why is Liesel the protagonist in The Book Thief?

An interesting question! To answer it, consider why Liesel makes a good protagonist in a literary sense.
The main reason is that she is a child. Much like Scout in To Kill a Mockingbird, Liesel has yet to reach the age where social and racial distinctions have much meaning. She is, in effect, a clean slate to build on for an author; she has no prior prejudices, no deeply ingrained beliefs or values. That is why, when dealing with difficult subjects such as racial or social prejudice, many great literary giants choose to have children as the protagonists. It gives them someone neutral, someone whom the audience can relate to and understand. Liesel is young enough to grow with the audience, to learn to have values, beliefs, and opinions, and to learn how to control those.
For instance, had the protagonist been Rosa or Hans or even Max, the story would not have progressed so naturally, because all of those characters already have ingrained values, opinions, and beliefs. By taking someone who is neutral, who along with the audience comes to understand everyone around her without prejudice, the story can grow naturally. It also helps the audience to relate to the protagonist, which is extremely important for a book to be successful.
Another important reason why Liesel is the protagonist is that she lives. She sees her whole world come to an end and yet still she survives. A major theme of the book is that life is a precarious balance of gains and losses, and Liesel manages to navigate this unsteady balance, giving the audience hope that they can too.