A path that is used by the public is considered public property. Therefore, if a path is used by the public passes through a private field, the owner may not take away the path. Such a scenario can happen if this path was always used, even before this owner came along and bought this field.
Furthermore, if the owner of the field decided to provide a path for the public on the edge of his field instead of the one running through the middle of his field, the public may use both the old and new paths. Even though this seems unfair to the owner, for after all, he has provided an alternate means to walk across his field, nevertheless, they may use both.
The reason Chazal instituted such a law is because they were afraid that the owner would provide a circuitous route, which would inconvenience the public. Another reason is that even if the new path is straight, it will still inevitably inconvenience some people. Since people from both sides of the field use this path, if it’s moved to the right, it will trouble those who come from the left, and vice versa.