You can choose to leave new issues unassigned. This can be achieved by altering the 'Allow Unassigned Issues' flag in the configuration options. To do this go to the General Configuration page of the Administration section. Now simply edit the configuration and turn the 'Allow Unassigned Issues' flag on. If a project already exists prior to making this change, please make sure to edit the project and change the "Default Assignee:" to be "Unassigned." Otherwise, the default assignee will continue to be whoever was originally assigned to the project. For more detail please refer to the documentation relating to this function.
This function is not enabled by default, as different companies tend to have different approaches to handling issues. We have found that many of our customers prefer to have issues always assigned to an owner, to ensure that somebody is responsible for its handling and resolution.